NCERT Solutions for Class 9 Science Chapter 12 Sound

NCERT Solutions for Class 9 Science Chapter 12 Sound

These Solutions are part of NCERT Solutions for Class 9 Science. Here we have given NCERT Solutions for Class 9 Science Chapter 12 Sound. LearnInsta.com provides you the Free PDF download of NCERT Solutions for Class 9 Science (Physics) Chapter 12 – Sound solved by Expert Teachers as per NCERT (CBSE) Book guidelines. All Chapter 12 – Sound Exercise Questions with Solutions to help you to revise complete Syllabus and Score More marks.

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NCERT TEXT BOOK QUESTIONS

IN TEXT QUESTIONS

Question 1.
Explain how sound is produced by your school bell.

                                                            Or

Sound is produced when your school bell is struck with a hammer. Why ? (CBSE 2011)
Answer:
When school bell is struck by a hammer, it starts vibrating. Since the vibrating bodies produce sound, so the vibrating school bell produces the sound.

Question 2.
Why are sound waves called mechanical waves ? (CBSE 2012)
Answer:
Sound waves are characterised by the motion of particles of a medium. Hence sound waves are called mechanical waves.

Question 3.
Suppose you and your friend are on the moon. Will you be able to hear any sound produced by your friend ?
Answer:
Sound waves need material medium like air to move from one place to another place. Since there is no air on the moon, so sound cannot travel from one place to another place. Hence, we cannot hear sound on the moon.

Question 4.
Which wave property determines
(a) loudness,
(b) pitch ? (CBSE 2011, 2012)
Answer:
(a) Amplitude of the wave determines loudness.
(b) Frequency of the wave determines pitch.

Question 5.
Guess which sound has a higher pitch : guitar or car horn ?
Answer:
Guitar, because frequency of sound produced by guitar is higher than the sound produced by car horn.

Question 6.
What are wavelength, frequency, time period and amplitude of a sound wave ? (CBSE 2012)
Answer:
Wavelength (or length of a wave): The distance between two successive regions of high pressure or high density {or compressions) or the distance between two successive regions of low pressure or low density (or rarefactions) is known as wavelength of a sound wave. It is denoted by λ (read as lambda).
In S.I., unit of wavelength is metre (m).
Frequency: The number of compressions or rarefactions crossing a point per unit time is known as the frequency of a sound wave. It is denoted by μ (read as Neu). In S.I., unit of frequency is hertz (Hz).
1 hertz = one oscillation completed by a vibrating body or a vibrating particle in one second.
Time period: Time taken by two consecutive compressions or rarefactions to cross a fixed point. Amplitude. The maximum displacement of a vibrating body from its rest position or mean position.

Question 7.
How are the wavelength and frequency of a sound wave related to its speed ? (CBSE 2011, 2012)
Answer:
V = vλ.

Question 8.
Calculate the wavelength of a sound wave whose frequency is 200 Hz and speed is 440 m/s in a given medium.
Answer:
NCERT Solutions for Class 9 Science Chapter 12 Sound image - 1

Question 9.
A person is listening to a tone of 500 Hz sitting at a distance of 450 m from the source of sound. What is the time interval between successive compressions from the source ?
Answer:
NCERT Solutions for Class 9 Science Chapter 12 Sound image - 2

Question 10.
Distinguish between loudness and intensity of sound.
Answer:

Loudness Intensity of a sound
1.Loudness is a subjective quantity. It depends upon the sensitivity of the human ear. A sound may be loud for a person but the same sound may be feeble for another person who is hard of hearing even when both are sitting at the same distance from the source of sound.

 

Intensity of a sound is an objective physical quantity. It does not depend on the sensitivity of a human ear.
 2. Loudness cannot be measured as a physical quantity because it is just sensation which can be felt only.

 

Intensity of a sound can be measured as a physical quantity.

Question 11.
In which of the three media, air, water or iron, does sound travel the fastest at a particular temperature ?
Answer:
Sound travels the fastest in iron.

Question 12.
An echo returned in 3 s. What is the distance of the reflecting surface from the source, given that the speed of sound is 342 m s-1 ? (CBSE 2011)
Answer:
Time taken by sound to travel from the source to the reflecting surface, t = 3/2 = 1.5 s
Speed, v = 342 m s
Distance of reflecting surface from the source, S = vt = 342 x 1.5 = 513 m.

Question 13.
Why are the ceilings of concert halls curved ? (CBSE 2011, 2012)
Answer:
So that the sound after reflection from the ceiling reaches all the corners of the hall.

Question 14.
What is the audible range of the average human ear ? (CBSE, 2011, 2012, 2015)
Answer:
20 Hz to 20,000 Hz.

Question 15.
What is the range of frequencies associated with :
(a) infra sound ?
(b) ultra sound ? (CBSE 2011, 2013)
Answer:
(a) Frequencies less than 20 Hz and greater than zero.
(b) Frequencies greater than 20,000 Hz and equal to 107 Hz.

Question 16.
A submarine emits a sonar pulse, which returns from an underwater cliff in 1.02 s. If the speed of sound in salt water is 1531 m/s, how far away is the cliff ?
Answer:
Time taken by the pulse to go from submarine to the cliff, t = 1.02/2 =0.51 s
Speed of sound, v = 1531 m/s
Distance of cliff from the submarine, S = vt = 1531 x 0.51 = 780.81 m.

NCERT CHAPTER END EXERCISE

Question 1.
What is sound and how is it produced ? (CBSE2012)
Answer:
Sound is a form of energy which produces the sensation of hearing in our ears. Sound is produced by forcing an object to vibrate. In other words, sound is produced by a vibrating object.

Question 2.
Why is sound wave called a longitudinal wave ? (CBSE 2012)
Answer:
When sound waves travel in medium, the particles of the medium vibrate about their equilibrium positions along the direction of the propagation of the waves.

Question 3.
Which characteristic of the sound helps you to identify your friend by his voice while sitting with others in a dark room ? (CBSE 2011)
Answer:
Timber or quality of sound.

Question 4.
Flash and thunder are produced simultaneously. But thunder is heard a few seconds after the flash is seen. Why ?

          Or

There is some time interval between observing a flash and hearing a thunder. Explain. (CBSE 2013)
Answer:
Thunder is heared after some time interval the flash is seen because speed of sound is less than the speed of light.

Question 5.
A person has a hearing range of 20 Hz to 20 kHz. What are the typical wavelengths of sound waves in air corresponding to these two frequencies ?
Answer:
Take the speed of sound.in air as 344 m s-1.
NCERT Solutions for Class 9 Science Chapter 12 Sound image - 3

Question 6.
Two children are at opposite ends of an aluminium rod. One strikes the end of the rod with a stone. Find the ratio of times taken by the sound waves in air and in the aluminium to reach the second child. (Speed of sound in aluminium is 6420 m s-1 and in air is 346 m s-1). (CBSE 2013)
Answer:
Let l = length of the rod
Time taken by sound to travel distance / in aluminium rod,
NCERT Solutions for Class 9 Science Chapter 12 Sound image - 4
NCERT Solutions for Class 9 Science Chapter 12 Sound image - 5

Question 7.
The frequency of a source of sound is 100 Hz. How many times does it vibrate in a minute ?
(CBSE 2011, 2012)
Answer:
Frequency of source = 100 Hz.
Number of times the source of sound vibrates in 1 s = 100
Number of times the source vibrates in a minute or 60 s = 100 x 60 = 6000.

Question 8.
Does sound follow the same laws of reflection as light does ? Explain.
Answer:
Yes. Sound waves are reflected just like light waves.

Question 9.
When a sound is reflected from a distant object, an echo is produced. Let the distance of the reflecting surface and the source of sound production remains the same. Do you hear echo sound on a hotter day ?
Answer:
Let d = distance between the reflecting surface and the source of sound
v = speed of sound in air.
NCERT Solutions for Class 9 Science Chapter 12 Sound image - 6
On a hotter day, speed of sound increases with increase in temperature. Hence, the time after which echo is heard decreases. If the time taken by the reflected sound is less than 0-1 s after the production of original sound, then echo is not heard. However, if this time is greater than 0-1 s, then echo will be heard.

Question 10.
Give two practical applications of multiple reflection of sound waves. (CBSE 2011, 2012)
Answer:

  1. Megaphone
  2. Hearing aid.

Question 11.
A stone is dropped from the top of a tower 500 m high into a pond,of water at the base of the tower. When is the splash heard at the top ? Given g = 10 m s-2 and speed of sound = 340 m s-1 .
(CBSE 2011, 2012)
Answer:
Time, after which splash is heard = time taken by the stone to reach the surface of water in a pond + time taken by the sound of splash to reach the top of tower.
NCERT Solutions for Class 9 Science Chapter 12 Sound image - 7
NCERT Solutions for Class 9 Science Chapter 12 Sound image - 8

Question 12.
A sound wave travels at a speed of 399 m s-1. If its wavelength is 1.5 m, what is the frequency of the wave ? Will it be audible ?
Answer:
NCERT Solutions for Class 9 Science Chapter 12 Sound image - 9
Since audible range of frequencies is 20 Hz to 20,000 Hz. Hence, the given frequency will not be audible.

Question 13.
What is reverberation ? How can it be reduced ? (CBSE 2012, 2014)
Answer:
The phenomenon of prolongation of original sound due to the multiple reflection of sound waves even after the source of sound stops producing sound is called reverberation.
Reverberation can be reduced by covering the roof and walls of a hall by sound absorbing materials.

Question 14.
What is loudness of sound ? What factors does it depend on ? (CBSE 2011)
Answer:
Loudness of a sound is a subjective quantity which causes unpleasant effect in our ear.
Loudness depends upon the amplitude of the vibrating body and the sensitivity of human ear.

Question 15.
Explain how bats use ultrasound to catch a prey. (CBSE 2011, 2012)

                                                  Or

Bats have no eyes, yet they can ascertain distances. (CBSE 2013)
Answer:
Bats can produce ultrasonic waves by flapping their wings. They can also detect these waves. The ultrasonic waves produced by the bats after reflection from the obstacles like buildings guide them to remain away from the obstacles during their flights. Hence, they can fly during night without hitting the obstacles. Bats also catch their prey during night with the help of ultrasonic waves. The ultrasonic waves produced by a bat spread out. These waves after reflecting from a prey say an insect reach the bat. Hence, the bat can easily locate its prey (Figure 24).
NCERT Solutions for Class 9 Science Chapter 12 Sound image - 10

Question 16.
A sonar device on a submarine sends out a signal and receives an echo 5 s later. Calculate the speed of sound in water if the distance of the object from the submarine is 3625 m. (CBSE 2011)
Answer:
NCERT Solutions for Class 9 Science Chapter 12 Sound image - 11

NCERT Solutions for Class 9 Science Chapter 12 Sound

Hope given NCERT Solutions for Class 9 Science Chapter 12 are helpful to complete your science homework.

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RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder VSAQS

RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder VSAQS

These Solutions are part of RD Sharma Class 9 Solutions. Here we have given RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder VSAQS

Other Exercises

Question 1.
Write the number of surface of a right circular cylinder.
Solution:
Three, two circular and one curved.

Question 2.
Write the ratio of total surface area to the curved surface area of a cylinder of radius r and height h.
Solution:
∵ Radius = r
and height = h
∴ Curved surface area = 2πrh
and total surface area = 2πr(h + r)
∴ Ratio = 2πr(h + r) : 2πrh
= h + r : h

Question 3.
The ratio between the radius of the base and height of a cylinder is 2 : 3. If its volume is 1617 cm3, find the total surface area of the cylinder.
Solution:
Ratio in radius and height of the cylinder = 2 : 3
Let radius (r) = 2x
Then height (h) = 3x
∴ Volume = πr2h
RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder VSAQS Q3.1
RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder VSAQS Q3.2

Question 4.
If the radii of two cylinders are in the ratio 2 : 3 and their heights are in the ratio 5 : 3, then find the ratio of their volumes.
Solution:
Ratio of radii of two cylinder = 2:3
Let radius of first cylinder (r1) = 2x
and second cylinder (r2) = 3x
and ratio in their heights = 5:3
Let height of first cylinder (h1) = 5y
and height of second (h2) = 3y
∴ Volume of the first cylinder =πr2h
= π x (2x)2 x 5y = 20πx2y
and volume of second cylinder = π(3x)2 x 3y = 27πx2y
Now ratio between then,
= 20πx2y: 21πx2y
= 20 : 27

Hope given RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder VSAQS are helpful to complete your math homework.

If you have any doubts, please comment below. Learn Insta try to provide online math tutoring for you.

NCERT Exemplar Solutions for Class 9 Science Chapter 11 Work, Power and Energy

NCERT Exemplar Solutions for Class 9 Science Chapter 11 Work, Power and Energy

These Solutions are part of NCERT Exemplar Solutions for Class 9 Science . Here we have given NCERT Exemplar Solutions for Class 9 Science Chapter 11 Work, Power and Energy

MULTIPLE CHOICE QUESTIONS

Question 1.
When a body falls freely towards the earth, then its total energy
(a) increases
(b) decreases
(c) remains constant
(d) first increases and then decreases,
Answer:
(c) Total energy = K.E. + P.E.
When a body falls freely, its K.E. increases and P.E. decreases but the sum of K.E and P.E. remains the same.

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Question 2.
A car is accelerated on a levelled road and attains a velocity 4 times of its initial velocity. In this process, the potential energy of the car
(a) does not change
(b) becomes twice to that of initial
(c) becomes 4 times that of initial
(d) becomes 16 times that of initial.
Answer:
(a). Potential energy does not depend on the velocity of a body.

Question 3.
In case of negative work, the angle between the force and displacement is
(a)
(b) 45°
(c) 90°
(d) 180°.
Answer:
(d) Explanation : W = FS cos θ. When θ = 180°, cos 180° = – 1 and W = – FS

Question 4.
An iron sphere of mass 10 kg has the same diameter as an aluminium sphere of mass is 3.5 kg. Both spheres are dropped simultaneously from a tower.
When they are 10 m above the ground, they have the same
(a) acceleration
(b) momenta
(c) potential energy
(d) kinetic energy.
Answer:
(a). Freely falling bodies moves with constant acceleration.

Question 5.
A girl is carrying a school bag of 3 kg mass on her back and moves 200 m on a levelled road. The work done against the gravitational force will be (g = 10 m s-2)
(a) 6 x 103 J
(b) 6 J
(c) 0.6 J
(d) zero.
Answer:
(d) Explanation : W = FS cos 90° = 0.

Question 6.
Which one of the following is not the unit of energy ?
(a) joule
(b) newton metre
(c) kiiowatt
(d) kolwatt hour.
Answer:
(c) It is the unit of power.

Question 7.
The work done on an object does not depend upon the
(a) displacement
(b) force applied
(c) angle between force and displacement
(d) initial velocity of the object.
Answer:
(d) W = FS cos θ.

Question 8.
Water stored in a dam possesses
(a) no energy
(b) electrical energy
(c) kinetic energy
(d) potential energy
Answer:
(d). The energy possessed by a body by virtue of its position is called potential energy.

Question 9.
A body is falling from a height h. After it has fallen a height h/2, it will possess
(a) only potential energy
(b) only kinetic energy
(c) half potential and half kinetic energy
(d) more kinetic and less potential energy.
Answer:
(c).

SHORT ANSWER QUESTIONS

Question 10.
A rocket is moving up with a velocity u. If the velocity of this rocket is suddenly tripled, what will be the ratio of two kinetic energies ?
Answer:
NCERT Exemplar Solutions for Class 9 Science Chapter 11 Work, Power and Energy image - 1

Question 11.
Avinash can run with a speed of 8 m s-1 against the frictional force of 10 N, and Kapil can move with a speed of 3 m s-1 against the frictional force of 25 N. Who is more powerful and why ?
Answer:
P = Fu
Power of Avinash = 10 x 8 = 80 W
Power of Kapil = 25 x 3 = 75 W
So, Avinash is more powerful.

Question 12.
A boy is moving on a straight road against a frictional force of 5 N. After travelling a distance of 1.5 km he forgot the correct path at a round about (Fig. 1) of radius 100 m.
NCERT Exemplar Solutions for Class 9 Science Chapter 11 Work, Power and Energy image - 2
Answer:
However, he moves on the circular path for one and half cycle and then he moves forward upto 2.0 km. Calculate the work done by him.
Here, F = 5N, Distance travelled S = 1500 + 3 π r + 2000 = 4442.86 m
W = F x S = 5 x 4442.86 = 22214.3 J.

Question 13.
Can any object have mechanical energy even if its momentum is zero ? Explain.
Answer:
NCERT Exemplar Solutions for Class 9 Science Chapter 11 Work, Power and Energy image - 3

Question 14.
Can any object have momentum even if its mechanical energy is zero ? Explain.
Answer:
NCERT Exemplar Solutions for Class 9 Science Chapter 11 Work, Power and Energy image - 4

Question 15.
The power of a motor pump is 2 kW. How much water per minute the pump can raise to a height of 10 m ? (Given g = 10 m s-2).
Answer:
NCERT Exemplar Solutions for Class 9 Science Chapter 11 Work, Power and Energy image - 5

Question 16.
The weight of a person on a planet A is about half that on the earth. He can jump upto 0.4 m height on the surface of the earth. How high he can jump on the planet A ?
Answer:
NCERT Exemplar Solutions for Class 9 Science Chapter 11 Work, Power and Energy image - 6

Question 17.
The velocity of a body moving in a straight line is increased by applying a constant force F, for some distance in the direction of the motion. Prove that the increase in the kinetic energy of the body is equal to the work done by the force on the body.
Answer:
Consider a body or an object of mass m moving with velocity u. Let a force F be applied on the body so that the velocity attained by the body after travelling a distance S is v (Figure 5).
NCERT Exemplar Solutions for Class 9 Science Chapter 11 Work, Power and Energy image - 7
Work done by the force on the body is given by
W =      FS                                                                               …(i)
Since velocity of the body changes so the body is accelerated. Let a be the acceleration of the body. Therefore, according to Newton’s second law of motion,
F =     ma                                                                             …(ii)
Using eqn. (ii) in eqn. (i), we get
NCERT Exemplar Solutions for Class 9 Science Chapter 11 Work, Power and Energy image - 8
Thus, work done by a force on a body is equal to the change in kinetic energy of the body This is known as work-energy theorem.

Question 18.
Is it possible that an object is in the state of accelerated motion due to external force acting on it, but no work is being done by the force. Explain it with an example.
Answer:
Yes. When body moves in a circular path.

Question 19.
A ball is dropped from a height of 10 m. If the energy of the ball reduces by 40% after striking the ground, how much high can the ball bounce back ? (g = 10 m s-2). (CBSE 2013)
Answer:
NCERT Exemplar Solutions for Class 9 Science Chapter 11 Work, Power and Energy image - 9

Question 20.
If an electric iron of 1200 W is used for 30 minutes everyday, find electric energy consumed in the month of April.
Answer:
Energy consumed in one day = P x t= 1200 W x ½ h = 600 Wh
Energy consumed in 30 days = 600 Wh x 30 = 1800 Wh =18 kWh.

LONG ANSWER QUESTIONS

Question 21.
A light and a heavy object have the same momentum. Find out the ratio of their kinetic energies. Which one has a larger kinetic energy ?
Answer:
NCERT Exemplar Solutions for Class 9 Science Chapter 11 Work, Power and Energy image - 10

Question 22.
An automobile engine propels a 1000 kg car (A) along a levelled road at a speed of 36 km h-1. Find power if the opposing frictional force is 100 N. Now, suppose after travelling a distance of 200 m, this car collides with another stationary car (B) of same mass and comes to rest. Let its engine also stops at the same time. Now car (B) starts moving on the same level road without getting its engine started. Find the speed of car (B) just after the collision.
Answer:
Force = 100 N, v = 36 km h-1 = 36 x (5/18) = 10 m s-1
Power, P = Force x velocity = 100 x 10 = 1000 W
According to law of conservation of linear momentum
Momentum of car A + Mementum of car B before collision = momentum of car A + momentum of car B after collision
i.e. 1000 x 10 + 1000 x 0 = 1000 x 0 + 1000 x v
 v = 10 m s-1
Thus, speed of car B just after collision =10 ms-1

Question 23.
A girl having mass of 35 kg sits on a trolley of mass 5 kg. The trolley is given an initial velocity of 4 ms-1 by applying a force. The trolley comes to rest after travelling a distance of 16m.
(a) How much work is done on the trolley ?
(b) How much work is done by the girl ?
Answer:
NCERT Exemplar Solutions for Class 9 Science Chapter 11 Work, Power and Energy image - 11

Question 24.
Four men lift a 250 kg box to a height of 1 m and hold it without raising or lowering it.
(a) How much work is done by the men in lifting the box ?
(b) How much work do they do in just holding it ?
(c) Why do they get tired while holding it ? (g = 10m s-2)
Answer:

Question 25.
(a) W = F x S = mgS= 250 x 10 x 1 =25.0 J.
(b) Zero. This is because displacement of box is zero.
(c) They get tired because muscular force applied by them is needed to balance the weight of the box.
Answer:
The Jog Falls in Karnataka State are nearly 200m high. 2000 tonnes of water falls from it in a minute. Calculate the equivalent power if all this energy can be utilized ? (g = 10 ms-2)
NCERT Exemplar Solutions for Class 9 Science Chapter 11 Work, Power and Energy image - 12

Question 26.
How is the power related to the speed at which a body can be lifted ? How many kilograms will a man working at the power of 100 W, be able to lift at constant speed of 1 ms-1 vertically ? (g = 10 ms-2)
Answer:
NCERT Exemplar Solutions for Class 9 Science Chapter 11 Work, Power and Energy image - 13

Question 27.
Define watt. Express kilowatt in terms of joule per second. A 150 kg car engine develops 500 W for each kg. What force does it exert in moving the car at a speed of 20 m s-1 ?
Answer:
NCERT Exemplar Solutions for Class 9 Science Chapter 11 Work, Power and Energy image - 14

Question 28.
Compare the power at which each of the following is moving upwards against the force of gravity ? (given g = 10 ms-2)

  1. a butterfly of mass 1.0 g that flies upward at a rate of 0.5 m s-1 .
  2. a 250 g squirrel climbing up on a tree at a rate of 0.5 m s-1.

Answer:

  1. P = Fv = mgv = 1 x 10-3 x 10 x 0.5 = 5 x 10-3 W
  2. P = Fv = mg= 250 x 10-3 x 10 x 0.5 = 1.25 W.

Hope given NCERT Exemplar Solutions for Class 9 Science Chapter 11 Work, Power and Energy are helpful to complete your science homework.

If you have any doubts, please comment below. Learn Insta try to provide online science tutoring for you.

RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.2

RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.2

These Solutions are part of RD Sharma Class 9 Solutions. Here we have given RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.2

Other Exercises

Question 1.
A soft drink is available in two packs – (i) a tin can with a rectangular base of length 5 cm and width 4 cm, having a height of 15 cm and
(ii) a plastic cylinder with circular base of diameter 7 cm and height 10 cm. Which container has greater capacity and by how much? [NCERT]
Solution:
In first case, in a rectangular container of soft drink, the length of base = 5 cm
and Width = 4 cm
Height = 15 cm
∴ Volume of soft drink = lbh = 5 x 4 x 15 = 300 cm3
and in second case, in a cylindrical container, diameter of base = 7 cm
RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.2 Q1.1
∴ The soft drink in second container is greater and how much greater = 385 cm – 380 cm2 = 85 cm2

Question 2.
The pillars of a temple are cylindrically shaped. If each pillar has a circular base of radius 20 cm and height 10 m. How much concrete mixture would be required to build 14 such pillars? [NCERT]
Solution:
Radius of each pillar (r) = 20 cm
RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.2 Q2.1

Question 3.
The inner diameter of a cylindrical wooden pipe is 24 cm and its outer diameter is 28 cm. The length of the pipe is 35 cm. Find the mass of the pipe, if 1 cm3 of wood has a mass of 0.6 gm. [NCERT]
Solution:
Inner diameter of a cylindrical wooden pipe = 24 cm
RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.2 Q3.1

Question 4.
If the lateral surface of a cylinder is 94.2 cm2 and its height is 5 cm, find:
(i) radius of its base
(ii) volume of the cylinder [Use π = 3.14] [NCERT]
Solution:
Lateral surface area of a cylinder = 94.2 cm2
RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.2 Q4.1

Question 5.
The capacity of a closed cylindrical vessel of height 1 m is 15.4 litres. How many square metres of metal sheet would be needed to make it? [NCERT]
Solution:
The capacity of a closed cylindrical vessel = 15.4 l
RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.2 Q5.1

Question 6.
A patient in a hospital is given soup daily in a cylindrical bowl of diameter 7 cm. If the bowl is filled with soup to a height of 4 cm, how much soup the hospital has to prepare daily to serve 250 patients? [NCERT]
Solution:
Diameter of the cylindrical bowl = 7 cm
∴ Radius (r) = \(\frac { 7 }{ 2 }\)cm
Level of soup in it = 4 cm
∴ Volume of soup in one bowl for one patient
RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.2 Q6.1

Question 7.
A hollow garden roller, 63 cm wide with a girth of 440 cm, is made of 4 cm thick iron. Find the volume of the iron.
Solution:
Width of hollow cylinder (A) = 63 cm
Girth = 440 cm
RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.2 Q7.1

Question 8.
The cost of painting the total outside surface of a closed cylindrical oil tank at 50 paise per square decimetre is ₹ 198. The height of the tank is 6 times the radius of the base of the tank. Find the volume corrected to 2 decimal places.
Solution:
Rate of painting = 50 paise per dm2
Total cost = ₹198
RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.2 Q8.1
RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.2 Q8.2

Question 9.
The radii of two cylinders are in the ratio 2 : 3 and their heights are in the ratio 5:3. Calculate the ratio of their volumes and the ratio of their curved surfaces.
Solution:
Ratio in radii of two cylinders = 2:3
and ratio in their heights = 5:3
Let radius of the first cylinder (r1) = 2x
and radius of second cylinder (r2) = 3x
and height of first cylinders (h1) = 5y
and height of second cylinder (h2) = 3y
(i) Now volume of the first cylinder = πr2h = π(2x)2 x 5y = 20πx22y
and volume of tlie second cylinder = π(3x)2 x 3y = π x 9×2 x 3y = 27πx2y
Now ratio in their volume
= 20πx2y : 21πx2y = 20 : 27
(ii) Curved surface area of first cylinder = 2πrh = 2π x 2x x 5y =20πxy
and curved surface area of second cylinder = 2π x 3x x = 1 8πxy
∴ Ratio in their curved surface area
= 20πxy : 18πxy = 10 : 9

Question 10.
The ratio between the curved surface area and the total surface area of a right circular cylinder is 1 : 2. Find the volume of the cylinder, if its total surface area is 616 cm2.
Solution:
Ratio in curved surface area and total surface area of a cylinder =1:2
Total surface area = 616 cm2
RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.2 Q10.1

Question 11.
The curved surface area of a cylinder is 1320 cm2 and its base had diameter 21 cm. Find the height and the volume of the cylinder. [Use π = 22/7]
Solution:
Curved surface area of a cylinder = 1320 cm2
Diameter of the base = 21 cm
RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.2 Q11.1

Question 12.
The ratio between the radius of the base and the height of a cylinder is 2 : 3. Find the total surface area of the cylinder, if its volume is 1617 cm3.
Solution:
Ratio between radius and height of a cylinder = 2:3
Volume =1617 cm3
Let radius (r) = 2x
Then height (h) = 3x
∴ Volume = πr2h
RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.2 Q12.1
RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.2 Q12.2

Question 13.
A rectangular sheet of paper, 44 cm x 20 cm, is rolled along its length of form a cylinder. Find the volume of the cylinder so formed.
Solution:
Length of sheet = 44 cm
Breadth = 20 cm
By rolling along length, the height of cylinder (h) = 20cm
and circumference of the base = 44cm
RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.2 Q13.1

Question 14.
The curved surface area of a cylindrical pillar is 264 m2 and its volume is 924 m3. Find the diameter and the height of the pillar.
Solution:
Curved surface area of a pillar = 264 m2
and volume = 924 m3
Let r be the radius and It be height, then 2πrh = 264
RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.2 Q14.1
RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.2 Q14.2

Question 15.
Two circular cylinders of equal volumes have their heights in the ratio 1 : 2. Find the ratio of their radii.
Solution:
Volumes of two cylinders are equal Ratio in their height h1 :h2 = 1: 2
RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.2 Q15.1

Question 16.
The height of a right circular cylinder is 10.5 m. Three times the sum of the areas of its two circular faces is twice the” area of the curved surface. Find the volume of the cylinder.
Solution:
Height of a right circular cylinder = 10.5 m
3 x sum of areas of two circular faces
= 2 x area of curved surface
Let r be that radius,
RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.2 Q16.1

Question 17.
How many cubic metres of earth must be dugout to sink a well 21 m deep and 6 m diameter? Find the cost of plastering the inner surface of the well at ₹9.50 per m2.
Solution:
Diameter of a well = 6 m
∴ Radius (r) = \(\frac { 6 }{ 2 }\) = 3 m
Depth (h) = 21 m
∴ Volume of earth dugout = πr2h
RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.2 Q17.1

Question 18.
The trunk of a tree is cylindrical and its circumference is 176 cm. If the length of the trunk is 3 m. Find the volume of the timber that can be obtained from the trunk.
Solution:
Circumference of a cylindrical trunk of a tree = 176 cm
RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.2 Q18.1

Question 19.
A cylindrical container with diameter of base 56 cm contains sufficient water to submerge a rectangular solid of iron with dimensions 32 cm x 22 cm x 14 cm. Find the rise in the level of the water when the solid is completely submerged.
Solution:
Diameter of cylindrical container = 56 cm
∴ Radius (r) = \(\frac { 56 }{ 2 }\) = 28 cm
Dimensions of a rectangular solid are = 32 cm x 22 cm x 14 cm
∴ Volume of solid = lbh
= 32 x 22 x 14 = 9856 cm3
∴ Volume of water in the container = 9856 cm3
Let h be the level of water, then
πr2h = 9856
RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.2 Q19.1

Question 20.
A cylindrical tube, open at both ends, is made of metal. The internal diameter of the tube is 10.4 cm and its length is 25 cm. The thickness of the metal is 8 mm everywhere. Calculate the volume of the metal.
Solution:
Length of metallic tube = 25 cm
Inner diameter = 10.4 cm
∴ Radius (r) = \(\frac { 10.4 }{ 2 }\) = 5.2 cm
Thickness of metal = 8 mm
∴ Outer radius (R) = 5.2 + 0.8 = 6.0 cm
Volume of metal used = π(R2 – r2) x h
RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.2 Q20.1

Question 21.
From a tap of inner radius 0.75 cm, water flows at the rate of 7 m per second. Find the volume in litres of water delivered by the pipe in one hour.
Solution:
Inner radius of a tap = 0.75 cm
Speed of flow of water in it = 7 m/s
Time = 1 hour
∴ Length of flow of water (h)
= 7 x 60 x 60 m = 25200 m
∴ Volume of water = πr2h
RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.2 Q21.1

Question 22.
A rectangular sheet of paper 30 cm x 18 cm can be transformed into the curved surface of a right circular cylinder in two ways i.e., either by rolling the paper along its length or by rolling it along its breadth. Find the ratio of the volumes of the two cylinders thus formed.
Solution:
Size of rectangular sheet = 30 cm x 18 cm
∴ Length of sheet = 30 cm
and breadth = 18 cm
By folding length wise,
Height = 18 cm
and circumference = 30 cm
RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.2 Q22.1
RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.2 Q22.2

Question 23.
How many litres of water flow out of a pipe having an area of cross-section of 5 cm2 in one minute, if the speed of water in the pipe is 30 cm/sec?
Solution:
Area of the cross-section of the pipe = 5 cm2
Speed of water flow = 30 cm/sec
Period = 1 minute
∴ Flow of water in 1 minute = 30 x 60 cm = 1800 cm
Area of mouth of pipe = 5 cm2
∴ Volume = 1800 x 5 = 9000 cm3
Volume of water in litres = 9000 ml
RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.2 Q23.1

Question 24.
Find the cost of sinking a tubewell 280 m deep, having diameter 3 m at the rate of ₹3.60 per cubic metre. Find also the cost of cementing its inner curved surface at ₹2.50 per square metre.
Solution:
Depth of well (h) = 280 m
Diameter = 3 m
RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.2 Q24.1

Question 25.
Find the length of 13.2 kg of copper wire of diameter 4 mm, when 1 cubic cm of copper weighs 8.4 gm.
Solution:
Weights of copper wire = 13.2 kg
Diamter = 4 mm
RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.2 Q25.1

Question 26.
A solid cylinder has a total surface area of 231 cm2. Its curved surface area is \(\frac { 2 }{ 3 }\) of the total surface area. Find the volume of the cylinder.
Solution:
Surface area of solid cylinder = 231 cm2
and curved surface area = \(\frac { 2 }{ 3 }\) of 231 cm2
RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.2 Q26.1
RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.2 Q26.2

Question 27.
A well with 14 m diameter is dug 8 m deep. The earth taken out of it has been evenly spread all around it to a width of 21 m to form an embankment. Find the height of the embankment.
Solution:
Diameter of a well = 14 m
∴ Radius (r) = y = 7 m
Depth (h) = 8 m
∴ Volume of the earth dugout = πr2h
RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.2 Q27.1
RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.2 Q27.2

Question 28.
The difference between inside and outside surfaces of a cylindrical tube 14 cm long is 88 sq. cm. If the volume of the tube is 176 cubic cm, find the inner and outer radii of the tube.
Solution:
Length of cylindrical tube = 14 cm
Difference betveen the outer surface and inner surface = 88 cm2
and volume of the tube = 176 cm3
Let R and r be the outer and inner radius of the tube
RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.2 Q28.1
RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.2 Q28.2

Question 29.
Water flows out through a circular pipe whose internal diameter is 2 cm, at the rate of 6 metres per second into a cylindrical tank. The radius of whose base is 60 cm. Find the rise in the level of water in 30 minutes?
Solution:
Internal diameter of the pipe = 2 cm
∴ Radius (r) = \(\frac { 2 }{ 2 }\) = 1 cm
Speed of water flow = 6m per second Water in 30 minutes (h) = 6 x 60 x 30 m = 10800 m
Volume of water = πr2h
RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.2 Q29.1

Question 30.
A cylindrical water tank of diameter 1.4 m and height 2.1 m is being fed by a pipe of diameter 3.5 cm through which water flows at the rate of 2 metre per second. In how much time the tank will be filled?
Solution:
Diameter of cylindrical tank = 1.4 m
∴ Radius (r) = \(\frac { 1.4 }{ 2 }\) = 0.7 m
and height (h) = 2.1 m
∴ Volume of water in the tank = πr2h
RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.2 Q30.1
RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.2 Q30.2

Question 31.
The sum of the radius of the base and height of a solid cylinder is 37 m. If the total surface area of the solid cylinder is 1628 m2. Find the volume of the cylinder.
Solution:
Sum of radius and height of a cylinder = 37 m
Let r be the radius and h be the height, then r + h = 37m …(i)
Total surface area of a solid cylinder = 1628m3
RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.2 Q31.1

Question 32.
A well with 10 m inside diameter is dug 8.4 m deep. Earth taken out of it is spread all around it to a width of 7.5 m to form an embankment. Find the height of the embankment.
Solution:
Diameter of the well = 10 m 10
∴ Radius (r) = \(\frac { 10 }{ 2 }\) = 5 m
Depth (h) = 8.4 m
∴ Volume of earth dugout = πr2h
RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.2 Q32.1

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RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.1

RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.1

These Solutions are part of RD Sharma Class 9 Solutions. Here we have given RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.1

Other Exercises

Question 1.
Curved surface area of a right circular cylinder is 4.4 m2. If the radius of the base of the cylinder is 0.7 m, find its height. [NCERT]
Solution:
Curved surface area of a cylinder = 4.4 m2
Radius (r) = 0.7 m
RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.1 Q1.1

Question 2.
In a hot water heating system, there is a cylindrical pipe of length 28 m and diameter 5 cm. Find the total radiating surface in the system. [NCERT]
Solution:
Diameter of the pipe = 5 cm
RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.1 Q2.1

Question 3.
A cylindrical pillar is 50 cm in diameter and 3.5 m in height. Find the cost of painting the curved surface of the pillar at the rate of 12.50 per m2. [NCERT]
Solution:
Diameter of cylindrical pillar = 50 cm
RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.1 Q3.1

Question 4.
It is required to make a closed cylindrical tank of height 1 m and base diameter 140 cm from a metal sheet. How many square metres of the sheet are required for the same? [NCERT]
Solution:
Height of cylinder (h) = 1 m = 100 cm
Diameter of box = 140 cm
RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.1 Q4.1

Question 5.
The total surface area of a hollow cylinder which is open from both sides is 4620 sq. cm, area of base ring is 115.5 sq. cm and height 7 cm. Find the thickness of the cylinder.
Solution:
Total surface area of a hollow cylinder open from both sides = 4620 cm2
Area of base of ring = 115.5 cm2
Height (h) = 7 cm
Let outer radius (R) = R
and inner radius = r
RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.1 Q5.1
RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.1 Q5.2
RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.1 Q5.3

Question 6.
Find the ratio between the total surface area of a cylinder to its curved surface area, given that its height and radius are 7.5 cm and 3.5 cm.
Solution:
Radius of the cylinder (r) = 3.5 cm
and height (h) = 7.5 cm
Total surface area = 2πr (h + r)
and curved surface area = 2πrh
RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.1 Q6.1

Question 7.
A cylindrical vessel, without lid, has to be tin-coated on its both sides. If the radius of the base is 70 cm and its height is 1.4 m, calculate the cost of tin-coating at the rate of ₹3.50 per 1000 cm2.
Solution:
Radius of the base of a cylindrical vessel (r) = 70 cm
and height (h) = 1.4 m = 140 cm
Total surface area (excluding upper lid) on both sides = 2πrh x 2 + πr2 x 2
RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.1 Q7.1

Question 8.
The inner diameter of a circular well is 3.5 m. It is 10 m deep. Find:
(i) inner curved surface area.
(ii) the cost of plastering this curved surface at the rate of ₹40 per m2. [NCERT]
Solution:
Inner diameter of a well = 3.5 m
RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.1 Q8.1

Question 9.
The students of a Vidyalaya were asked to participate s a competition for making and decorating pen holders in the shape of a cylinder with a base, using cardboard. Each pen holder was to be of radius 3 cm and height 10.5 cm. The Vidyalaya was to supply the competitors with cardboard. If there were 35 competitors, how much cardboard was required to be bought for the competition? [NCERT]
Solution:
Radius of cylinderical pen holder (r) = 3 cm
Height (h) = 10.5 cm
∴ Surface area of the pen holder
RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.1 Q9.1

Question 10.
The diameter of roller 1.5 m long is 84 cm. If it takes 100 revolutions to level a play¬ground, find the cost of levelling this ground at the rate of 50 paise per square metre.
Solution:
Diameter of a roller = 1.5 m
∴ Radius = \(\frac { 1.5 }{ 2 }\) = 0.75 m = 75 cm
and length (h) = 84 cm
RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.1 Q10.1

Question 11.
Twenty cylindrical pillars of the Parliament House are to be cleaned. If the diameter of each pillar is 0.50 m and height is 4 m. What will be the cost of cleaning them at the rate of ₹2.50 per square metre? [NCERT]
Solution:
Number of pillars = 20
Diameter of one pillar = 0.50 m
RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.1 Q11.1

Question 12.
A solid cylinder has total surface area of 462 cm2. Its curved surface area is one- third of its total surface area. Find the radius and height of the cylinder.
Solution:
Total surface of solid cylinder = 462 cm2
Curved surface area = \(\frac { 1 }{ 3 }\) of total surface area
RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.1 Q12.1

Question 13.
The total surface area of a hollow metal cylinder, open at both ends of external radius 8 cm and height 10 cm is 338 π cm2. Taking r to be inner radius, obtain an equation in r and use it to obtain the thickness of the metal in the cylinder.
Solution:
Total surface area of a hollow metal cylinder = 338π cm2
Let R be the outer radius, r be inner radius and h be the height of the cylinder of the cylinder
∴ 2πRh + 2πrh + 2πR2 – 2πr2 = 338π
R = 8 cm, h = 10 cm
⇒ 2πh (R + r) + 2π(R2 – r2) = 338π
⇒ Dividing by 2π , we get
⇒ h(R + r) + (R2 – r2) = 169
⇒ 10(8 + r) + (8 + r) (8 – r) = 169
⇒ 80 + 10r + 64 – r2 = 169
⇒ 10r – r2 + 144 – 169 = 0
⇒ r2 – 10r + 25 = 0
⇒ (r-5)2 = 0
⇒ r = 5
∴ Thickness of the metal = R – r = 8 – 5 = 3 cm

Question 14.
Find the lateral curved surface area of a cylinderical petrol storage tank that is 4.2m in diameter and 4.5 m high. How much steel was actually used, if \(\frac { 1 }{ 12 }\) of steel actually used was wasted in making the closed tank? [NCERT]
Solution:
Diameter of a cylinderical tank = 4.2 m
RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.1 Q14.1
RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.1 Q14.2

 

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RD Sharma Class 9 Solutions Chapter 18 Surface Areas and Volume of a Cuboid and Cube MCQS

RD Sharma Class 9 Solutions Chapter 18 Surface Areas and Volume of a Cuboid and Cube MCQS

These Solutions are part of RD Sharma Class 9 Solutions. Here we have given RD Sharma Class 9 Solutions Chapter 18 Surface Areas and Volume of a Cuboid and Cube MCQS

Other Exercises

Mark correct alternative in each of the following:
Question 1.
The length of the longest rod that can be fitted in a cubical vessel of edge 10 cm long, is
(a) 10 cm
(b) 10\(\sqrt { 2 } \) cm
(c) 10\(\sqrt { 3 } \) cm
(d) 20 cm
Solution:
Edge of cuboid (a) = 10 cm
∴ Longest edge = \(\sqrt { 3 } \) a cm
= \(\sqrt { 3 } \) x 10 = 10\(\sqrt { 3 } \) cm (c)

Question 2.
Three equal cubes are placed adjacently in a row. The ratio of the total surface area of the resulting cuboid to that of the sum of the surface areas of three cubes, is
(a) 7 : 9
(b) 49 : 81
(c) 9 : 7
(d) 27 : 23
Solution:
Let a be the side of three equal cubes
∴ Surface area of 3 cubes
= 3 x 6a2 = 18a2
and length of so formed cuboid = 3a
Breadth = a
and height = a
∴ Surface area = 2(lb + bh + hl)
= 2[3a x a + a x a+a x 3a] = 2[3a2 + a2 + 3a2] = 2 x 7a2 = 14a2
∴ Ratio in the surface areas of cuboid and three cubes = 14a2 : 18a2= 7:9 (a)

Question 3.
If the length of a diagonal of a cube is 8 \(\sqrt { 3 } \) cm, then its surface area is
(a) 512 cm2
(b) 384 cm2
(c) 192 cm2
(d) 768 cm2
Solution:
Length of the diagonal of cube = 8 \(\sqrt { 3 } \) cm
RD Sharma Class 9 Solutions Chapter 18 Surface Areas and Volume of a Cuboid and Cube MCQS Q3.1

Question 4.
If the volumes of two cubes are in the ratio 8:1, then the ratio of their edges is
(a) 8 : 1
(b) 2\(\sqrt { 2 } \) : 1
(c) 2 : 1
(d) none of these
Solution:
Let volume of first cube = 8x3
and of second cube = x3
RD Sharma Class 9 Solutions Chapter 18 Surface Areas and Volume of a Cuboid and Cube MCQS Q4.1

Question 5.
The volume of a cube whose surface area is 96 cm2, is
(a) 16\(\sqrt { 2 } \) cm3
(b) 32 cm3
(c) 64 cm3
(d) 216 cm3
Solution:
Surface area of a cube = 96 cm2
RD Sharma Class 9 Solutions Chapter 18 Surface Areas and Volume of a Cuboid and Cube MCQS Q5.1

Question 6.
The length, width and height of a rectangular solid are in the ratio of 3 : 2 : 1. If the volume of the box is 48 cm3, the total surface area of the box is
(a) 27 cm2
(b) 32 cm2
(c) 44 cm2
(d) 88 cm2
Solution:
Ratio in the dimensions of a cuboid =3 : 2 : 1
Let length = 3x
Breadth = 2x
and height = x
Then volume = lbh = 3x x 2x x x = 6×3
∴ 6x3 = 48 ⇒ x3= \(\frac { 48 }{ 6 }\) = 8 = (2)3
∴ x = 2
∴ Length (l) = 3 x 2 = 6 cm
Breadth (b) = 2 x 2 = 4 cm
Height (h) = 1 x 2 = 2 cm
Now surface area = 2[lb + bh + hl]
= 2[6 x 4 + 4 x 2 + 2 x 6] cm2
= 2[24 + 8-+ 12] = 2 x 44 cm2
= 88 cm2 (d)

Question 7.
If the areas of the adjacent faces of a rectangular block are in the ratio 2:3:4 and its volume is 9000 cm3, then the length of the shortest edge is
(a) 30 cm
(b) 20 cm
(c) 15 cm
(d) 10 cm
Solution:
Ratio in the areas of three adjacent faces of a cuboid = 2 : 3 : 4
Volume = 9000 cm3
Let the area of faces be 2x, 3x, Ax and
Let a, b, and c be the dimensions of the cuboid, then
∴ 2x = ab, 3x = be, 4x = ca
∴ ab x be x ca = 2x x 3x x 4x
a2b2c2 = 24 x 3
But volume = abc = 9000 cm3
RD Sharma Class 9 Solutions Chapter 18 Surface Areas and Volume of a Cuboid and Cube MCQS Q7.1
RD Sharma Class 9 Solutions Chapter 18 Surface Areas and Volume of a Cuboid and Cube MCQS Q7.2

Question 8.
If each edge of a cube, of volume V, is doubled, then the volume of the new cube is
(a) 2V
(b) 4V
(c) 6V
(d) 8V
Solution:
Let a be the edge of a cube whose Volume = V
∴ a3 = V
By doubling the edge, we get 2a
Then volume = (2a)3 = 8a3
∴ Volume of new cube = 8a3 = 8V (d)

Question 9.
If each edge of a cuboid of surface area S is doubled, then surface area of the new cuboid is
(a) 2S
(b) 4S
(c) 6S
(d) 8S
Solution:
Let each edge of a cube = a
Then surface area = 6a2
∴ S = 6a2
Now doubling the edge, we get
New edge of a new cube = 2a
∴ Surface area = 6(2a)2
= 6 x 4a2 = 24a2
= 4 x 6a2 = 4S (b)

Question 10.
The area of the floor of a room is 15 m2. If its height is 4 m, then the volume of the air contained in the room is
(a) 60 dm3
(b) 600 dm3
(c) 6000 dm3
(d) 60000 dm3
Solution:
Area of a floor of a room = 15 m2
Height (h) = 4 m
∴ Volume of air in the room = Floor area x Height
= 15 m2 x 4 m = 60 m3
= 60 x 10 x 10 x 10 dm2 = 60000 dm2 (d)

Question 11.
The cost of constructing a wall 8 m long, 4 m high and 20 cm thick at the rate of ₹25 per m3 is
(a) ₹16
(b) ₹80
(c) ₹160
(d) ₹320
Solution:
Length of wall (l) = 8 m
Breadth (b) = 20 cm = \(\frac { 1 }{ 5 }\) m
Height (h) = 4 m
RD Sharma Class 9 Solutions Chapter 18 Surface Areas and Volume of a Cuboid and Cube MCQS Q11.1

Question 12.
10 cubic metres clay in uniformaly spread on a land of area 10 acres. The rise in the level of the ground is
(a) 1 cm
(b) 10 cm
(c) 100 cm
(d) 1000 cm
Solution:
Volume of clay = 10 m3
Area of land = 10 acres
= 10 x 100 = 1000 m2
∴ Rise of level by spreading the clay
RD Sharma Class 9 Solutions Chapter 18 Surface Areas and Volume of a Cuboid and Cube MCQS Q12.1

Question 13.
Volume of a cuboid is 12 cm3. The volume (in cm3) of a cuboid whose sides are double of the above cuboid is
(a) 24
(b) 48
(c) 72
(d) 96
Solution:
Volume of cuboid = 12 cm3
By doubling the sides of the cuboid the
volume will be = 12 cm3 x 2 x 2 x 2
= 96 cm3 (d)

Question 14.
If the sum of all the edges of a cube is 36 cm, then the volume (in cm3) of that cube is
(a) 9
(b) 27
(c) 219
(d) 729
Solution:
Sum of all edges of a cube = 36 cm
No. of edge of a cube are 12
∴ Length of its one edge = \(\frac { 36 }{ 12 }\) = 3 cm
Then volume = (edge)3 = (3)3 cm3
= 27 cm3 (b)

Question 15.
The number of cubes of side 3 cm that can be cut from a cuboid of dimensions 9 cm x 9 cm x 6 cm, is
(a) 9
(b) 10
(c) 18
(d) 20
Solution:
Dimensions of a cuboid = 9 cm x 9 cm x 6 cm
RD Sharma Class 9 Solutions Chapter 18 Surface Areas and Volume of a Cuboid and Cube MCQS Q15.1

Question 16.
On a particular day, the rain fall recorded in a terrace 6 m long and 5 m broad is 15 cm. The quantity of water collected in the terrace is
(a) 300 litres
(b) 450 litres
(c) 3000 litres
(d) 4500 litres
Solution:
Dimension of a terrace = 6mx5m
Level of rain on it = 15 cm
∴ Volume of water collected on it
RD Sharma Class 9 Solutions Chapter 18 Surface Areas and Volume of a Cuboid and Cube MCQS Q16.1

Question 17.
If A1, A2 and A3 denote the areas of three adjacent faces of a cuboid, then its volume is
RD Sharma Class 9 Solutions Chapter 18 Surface Areas and Volume of a Cuboid and Cube MCQS Q17.1
Solution:
Let l, b, h be the dimensions of the cuboid
∴ A1= lb, A2 = bh, A3 = hl
∴ A1 A2 A3 = lb.bh.hl = l2b2h2
RD Sharma Class 9 Solutions Chapter 18 Surface Areas and Volume of a Cuboid and Cube MCQS Q17.2

Question 18.
If l is the length of a diagonal of a cube of volume V, then
RD Sharma Class 9 Solutions Chapter 18 Surface Areas and Volume of a Cuboid and Cube MCQS Q18.1
Solution:
Volume of a cube = V
and longest diagonal = l
RD Sharma Class 9 Solutions Chapter 18 Surface Areas and Volume of a Cuboid and Cube MCQS Q18.2

Question 19.
If V is the volume of a cuboid of dimensions x, y, z and A is its surface area, then \(\frac { A }{ V }\)
RD Sharma Class 9 Solutions Chapter 18 Surface Areas and Volume of a Cuboid and Cube MCQS Q19.1
Solution:
A is surface area, V is volume and x, y and z are the dimensions
Then V = xyz
A = 2[xy + yz + zx]
RD Sharma Class 9 Solutions Chapter 18 Surface Areas and Volume of a Cuboid and Cube MCQS Q19.2

Question 20.
The sum of the length, breadth and depth of a cuboid is 19 cm and its diagonal is 5\(\sqrt { 5 } \) cm. Its surface area is
(a) 361 cm2
(b) 125 cm2
(c) 236 cm2
(d) 486 cm2
Solution:
Let x, y, z be the dimensions of a cuboid,
then x + y + z = 19 cm
RD Sharma Class 9 Solutions Chapter 18 Surface Areas and Volume of a Cuboid and Cube MCQS Q20.1

Question 21.
If each edge of a cube is increased by 50%, the percentage increase in its surface area is
(a) 50%
(b) 75%
(c) 100%
(d) 125%
Solution:
Let in first case, edge of a cube = a
Then surface area = 6a2
In second case, increase in side = 50%
RD Sharma Class 9 Solutions Chapter 18 Surface Areas and Volume of a Cuboid and Cube MCQS Q21.1

Question 22.
A cube whose volume is 1/8 cubic centimeter is placed on top of a cube whose volume is. 1 cm3. The two ,cubes are then placed on top of a third cube whose volume is 8 cm3. The height of the stacked cubes is
(a) 3.5 cm
(b) 3 cm
(c) 7 cm
(d) none of these
Solution:
Volume of first cube = \(\frac { 1 }{ 2 }\) cm3
RD Sharma Class 9 Solutions Chapter 18 Surface Areas and Volume of a Cuboid and Cube MCQS Q22.1

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Value Based Questions in Science for Class 9 Chapter 11 Work, Power and Energy

Value Based Questions in Science for Class 9 Chapter 11 Work, Power and Energy

These Solutions are part of Value Based Questions in Science for Class 9. Here we have given Value Based Questions in Science for Class 9 Chapter 11 Work, Power and Energy

VALUE BASED QUESTIONS

Question 1.
Akshit is a student of class IX. He was waiting for a bus on a bus stand. He saw an old man trying to keep his box on the roof of a bus but was unable to do so. Akshit picked up his box and placed the box on the roof of the bus. The old man thanked Akshit.
Answer the following questions based on the above paragraph.

  1. Is the work done by Akshit while placing the box on the roof of the bus positive or negative ?
  2. Is the work done by gravity on the box is positive or negative ?
  3. What values are shown by Akshit ?

Answer:

  1. Positive,
  2. Negative,
  3. Akshit is helpful. He believes in helping old people. He has dignity of labour.

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Question 2.
Rajiv is a student of class IX. He bought a toy gun from the market. The bullets used in gun were made of rubber. His mother asked Rajiv not to fire bullets on the window panes. Rajiv went to a park and fired bullets on a displaying screen made of plastic. Rajiv’s friend Rohan objected the action of Rajiv. Rajiv started quarelling with Rohan.
Answer the following questions based on above paragraph.

  1. Name the type of energy stored in the spring of gun.
  2. Name the type of energy of a moving bullet.
  3. What values are shown by Rohan ?
  4. Comment on the attitude of Rajiv.

Answer:

  1. Elastic potential energy,
  2. Kinetic energy.
  3. According to Rohan, one must not destroy or disfigure the public or private property. It is sin and crime.
  4. Rajiv’s attitude is undesirable. He has no right to destroy the public property. He must be ashamed of his action.

Question 3.
Ramesh was walking on a road in the morning. He found that an old mail was lying on a road side. Ramesh touched the body of the old man. His body was very cold. Ramesh rubbed the hands and feet of the old man. The old man opened his eye. Ramesh helped the old man to reach his home.
Answer the following questions based on above paragraph.

  1. Why hands become warm, when rubbed ?
  2. What values are shown by Ramesh ?

Answer:

  1. When hands are rubbed against each other, mechanical energy is converted into heat energy. Therefore, hands become warm.
  2. Ramesh is helpful, feels concerned for others. He has high degree of general awareness.

Question 4.
An old man was standing on a bus stand carrying a very heavy luggage. Saurabh was looking at the old man and finding him uncomfortable, requested him to put down the luggage and helped him in doing so.
(a) Did the old man do any work while holding the luggage ?
(b) What is the equation for work done against gravity ?
(c) Why did Saurabh ask the old man to put down the luggage ? (CBSE 2015)
Answer:
(a) No work is done by the old man.
(b) W = mgh
(c) Saurabh is a good boy. He always helps needy and old people. He wanted to help the old man and hence asked him to put down the luggage.

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NCERT Solutions for Class 9 Science Chapter 11 Work, Power and Energy

NCERT Solutions for Class 9 Science Chapter 11 Work, Power and Energy

These Solutions are part of NCERT Solutions for Class 9 Science. Here we have given NCERT Solutions for Class 9 Science Chapter 11 Work, Power and Energy. LearnInsta.com provides you the Free PDF download of NCERT Solutions for Class 9 Science (Physics) Chapter 11 – Work and Energy solved by Expert Teachers as per NCERT (CBSE) Book guidelines. All Chapter 11 – Work and Energy Exercise Questions with Solutions to help you to revise complete Syllabus and Score More marks.

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NCERT TEXT BOOK QUESTIONS

IN TEXT QUESTIONS

Question 1.
A force of 7 N acts on an object. The displacement is say 8 m in the direction of the force. Let us take it that the force acts on the object through the displacement. What is the work done in this case ?
(CBSE 2011)
Answer:
Here, Force, F = 7 N
Displacement, S = 8 m
Work done = F x S = 7 x 8 = 56 J.

Question 2.
When do we say that work is done ? (CBSE 2012)
Answer:
Work is done, when force acts on an object and the object is displaced from its initial position.

Question 3.
Write an expression for the work done when a force is acting on an object in the direction of its displacement.
Answer:
W = FS

Question 4.
Define 1 J of work. (CBSE 2012)

                                           Or

Define SI unit of work. (CBSE Sample Paper 2010 ; CBSE 2011, 2012)
Answer:
Work is said to be 1 J if 1N force displaces an object through 1 metre in its own direction.

Question 5. 
A pair of bullocks exerts a force of 140 N on a plough. The field being ploughed is 15 m long. How much work is done in ploughing the length of the field ? (CBSE 2010)
Answer:
Here, Force, F = 140 N
Displacement, S = 15 m
Work done = F x S = 140 x 15 = 2100 J.

Question 6.
What is the kinetic energy of an object ? (CBSE 2011, 2012, 2014, 2015)
Answer:
The energy possessed by an object by virtue of its motion is known as the kinetic energy of the object.

Question 7.
Write an expression for the kinetic energy of an object.
Answer:
K.E. of an object = 1/2 mv2 , where m is the mass of the object and v is the speed of the object.

Question 8.
The kinetic energy of an object of mass m moving with a velocity of 5 m s-1 is 25 J. What will be its kinetic energy when its velocity is doubled ? What will be its kinetic energy when its velocity is increased
(CBSE 2010, 2012)
Answer:
NCERT Solutions for Class 9 Science Chapter 11 Work, Power and Energy image - 1

Question 9.
What is power ?
Answer:
Power is defined as the rate of doing work.

Question 10.
Define 1 Watt of power.
Define SI unit of power.
Answer:
Power of an agent is said to be 1 watt if it does 1 joule work in 1 second.

Question 11.
A lamp consumes 1000 J of electrical energy in 10 s. What is its power ?
Answer:
NCERT Solutions for Class 9 Science Chapter 11 Work, Power and Energy image - 2

Question 12.
Define average power.
Answer:
Average power is defined as the ratio of total work done by an agent to the total time taken.

NCERT CHAPTER END EXERCISE

Question 1.
Look at the activities listed below. Reason out whether or not work is done in the light of your understanding of the term ‘work.’
(a) Suma is swimming in a pond.
(b) A donkey is carrying a load on its back.
(c) A wind mill is lilting water from a well.
(d) A great plant is carrying out photosynthesis.
(e) An engine is pulling a train.
(f) Food grains are getting dried in the sun.
(g) A sailboat is moving due to wind energy.
Answer:
(a) Work is done (Reaction (Force) of water on Suma during swimming displaces Suma in the forward direction).
(b) No work is done (Force of gravity acting on the load is perpendicular to the displacement of the load).
(c) Work is done (Force displaces water in the upward direction).
(d) No work is done (There is no force and no displacement during photosynthesis).
(e) Work is done (Force displaces the train.)
(f) No work is done (There is no external force and no displacement of the grains.)
(g) Work is done (Force acting on the sail boat displaces the boat).

Question 2.
An object thrown at a certain angle to the ground moves in a curved path and falls back to the ground.
The initial and the final points of the path of the object lie on the same horizontal line. What is the work done by the force of gravity on the object ? (CBSE 2011, 2012)
Answer:
Work done by the force of gravity on the object = mgh
Here, h = difference in height of the initial and final positions of the object.
Since, initial and final positions of the object are at the same level, so h = 0.
∴ Work done = mg x 0 = 0.

Question 3.
A battery lights a bulb. Describe the energy change involved in the process. (CBSE 2012)
Answer:
The chemical energy of the battery changes into electrical energy which is then converted into light energy and heat energy.

Question 4.
Certain force acting on a 20 kg mass changes its velocity from 5 m s-1 to 2 m s-1. Calculate the work done by the force. (CBSE 2011, 2012)
Answer:
NCERT Solutions for Class 9 Science Chapter 11 Work, Power and Energy image - 3

Question 5.
A mass of 10 kg is at a point A on a table. It is moved to a point B which is at a distance of 2 m from A.
If the line joining A and B is horizontal, what is the work done on the object by the gravitational force ? Explain your answer. (CBSE 2012)
Answer:
Work done by the gravitational force = mgh
Since h = 0 (because both points A and B are at the same height.)
Work done = 0.

Question 6.
The potential energy of a freely falling object decreases progressively. Does this violate the law of conservation of energy ? Why ? (CBSE 2011)
Answer:
No, As the potential energy of a freely falling object decreases, the object acquires more and more speed. So the kinetic energy of the object increases at the cost of its potential energy. However, total energy of the object remains the same at every point.

Question 7.
What are the various energy transformations that occur when you are riding a bicycle ?
Answer:
Our muscular energy is converted into the kinetic energy of the bicycle.

Question 8.
Does the transfer of energy takes place when you push a huge rock with all your might and fail to move it ? Where is the energy you spend going ?
Answer:
When we push a huge rock, the rock also exerts a huge force on us. The muscular energy spent by us is used to oppose the huge force acting on us due to the rock.

Question 9.
A certain household has consumed 250 units of energy during a month. How much energy is this in joules ?
Answer:
NCERT Solutions for Class 9 Science Chapter 11 Work, Power and Energy image - 4

Question 10.
An object of mass 40 kg is raised to a height of 5 m above the ground. What is its potential energy ? If the object is allowed to fall, find its kinetic energy when it is half-way down. (CBSE 2011)
Answer:

  1. Potential energy = mgh
    = 40 kg x 10 m s-2 x 5 m = 2000 J.
  2. According to the law of conservation of energy :
    K.E. when it is half-way down = P.E. when it is half-way down
    NCERT Solutions for Class 9 Science Chapter 11 Work, Power and Energy image - 5

Question 11.
What is the work done by the force of gravity on a satellite moving round the earth ? Justify your answer. (CBSE 2012)
NCERT Solutions for Class 9 Science Chapter 11 Work, Power and Energy image - 6
Answer:
The force of gravity acting on a satellite moves the satellite in a circular path. Since, the force of gravity acts at right angle to the displacement of the satellite (Figure), so work done,
W = FS cos 90° = 0

Question 12.
Can there be displacement of an object in the absence of any force acting on it ?
Answer:
Yes, When an object moves with a constant velocity, then no force acts on the object. However, the object is displaced from one position to another position.

Question 13.
A person holds a bundle of hay over his head for 30 minutes and gets tired. Has he done some work or not? Justify your answer. (CBSE 2011, 2012)
Answer:
Work = Force x Displacement.
Since the person is at rest, so displacement = 0.
Hence no work is done by the person.

Question 14.
An electric heater is rated 1500 W. How much energy does it use in 10 hours ? (CBSE 2011, 2012)
Answer:
NCERT Solutions for Class 9 Science Chapter 11 Work, Power and Energy image - 7

Question 15.
Illustrate the law of conservation of energy by discussing the energy changes which occur when we draw a pendulum bob to one side and allow it to oscillate. Why does the bob eventually come to rest ? What happens to its energy eventually ? Is it a violation of the law of conservation of energy ?
Answer:
For part

  1. Consider a simple pendulum suspended from a rigid support at S. Let OS be the undisturbed position of the pendulum. Now, let the pendulum be displaced to position A where it is at rest (Figure 9).
    NCERT Solutions for Class 9 Science Chapter 11 Work, Power and Energy image - 8
    At position A, the pendulum has potential energy (mgh). When the pendulum is released from position A, it begins to move towards position O. The speed of the bob of the pendulum increases and its height decreases. So potential energy of the pendulum is changed into its kinetic energy. At position O, whole of the potential energy of the pendulum is converted to its kinetic energy.
  2. When the bob of a simple pendulum oscillates in air, the air friction opposes its motion. The kinetic energy of the oscillating bob is used to overcome the air friction which tries to oppose the motion of the bob of the pendulum. As the oscillating bob strikes the air molecules, the kinetic energy of the bob of the pendulum is converted into heat energy. This heat energy is transferred to the atmosphere. In other words, the kinetic energy of the bob of the pendulum is converted into heat energy with the passage of time. Ultimately, the entire kinetic energy of the bob is converted into heat energy and hence the oscillating bob comes to rest. In this case, the law of conservation of energy is not violated as one form of energy is converted into another form of energy.

Question 16.
An object of mass m is moving with a constant velocity v. How much work should be done on the object in order to bring the object to rest ? (CBSE 2012)
Answer:
NCERT Solutions for Class 9 Science Chapter 11 Work, Power and Energy image - 9

Question 17.
Calculate the work required to be done to stop a car of 1500 kg moving at a velocity of 60 km/h. (CBSE 2011, 2016)
Answer:
NCERT Solutions for Class 9 Science Chapter 11 Work, Power and Energy image - 10

Question 18.
In each of the following, a force F is acting on an object of mass, m. The direction of displacement is from west to east shown by the longer arrow. Observe the diagrams carefully and state whether the work done by the force is negative, positive or zero. (CBSE 2011)
NCERT Solutions for Class 9 Science Chapter 11 Work, Power and Energy image - 11
Answer:
First Case: Angle between force and displacement, 0 = 90°
∴ work done = FS cos 6 = FS cos 90° = 0
Second Case: Angle between force and displacement, 0 = 0°
work done = FS cos 9 = FS cos 0° = FS ( positive work) (∴ cos 0° = 1)
Third Case: Angie between force and displacement, 9 = 180°
work done = FS cos 9 = FS cos 180° = -FS ( negative work) (∴ cos 180° = -1)

Question 19.
Soni says that the acceleration in an object could be zero even when several forces are acting on it. Do you agree with him ? Why ?
Answer:
Yes, If the sum of several forces acting on an object is zero, then net force acting on it is zero. Hence,
NCERT Solutions for Class 9 Science Chapter 11 Work, Power and Energy image - 12

Question 20.
Find the energy in kWh consumed in 10 hours by four devices of power 500 W each.
Answer:
Total power, P = 500 W x 4 = 2000 W
Time, t = 10 h
Energy consumed = Power x Time
= 2000 W x 10 h = 20,000 Wh = 20 kWh.

Question 21.
A freely falling object eventually stops on reaching the ground. What happens to its kinetic energy ?
(CBSE 2011)
Answer:
Kinetic energy is converted into sound energy and heat energy.

NCERT Solutions for Class 9 Science Chapter 11 – Work and Energy

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RD Sharma Class 9 Solutions Chapter 18 Surface Areas and Volume of a Cuboid and Cube VSAQS

RD Sharma Class 9 Solutions Chapter 18 Surface Areas and Volume of a Cuboid and Cube VSAQS

These Solutions are part of RD Sharma Class 9 Solutions. Here we have given RD Sharma Class 9 Solutions Chapter 18 Surface Areas and Volume of a Cuboid and Cube VSAQS

Other Exercises

Question 1.
If two cubes of side 6 cm are joined face to face, then find the volume of the resulting cuboid.
Solution:
Side of a cube = 6 cm
∴ By joining two such cubes, the length of so
formed cuboid (l) = 6 x 2 = 12 cm
Breadth (b) = 6 cm
Height (h) = 6 cm
∴ Volume = lbh = 12 x 6 x 6 cm3
= 432 cm3

Question 2.
Three cubes of metal whose edges are in the ratio 3 : 4 : 5, are melted down into a single cube whose diagonals is 12 \(\sqrt { 3 } \) cm. Find the edges of three cubes.
Solution:
Ratio in the sides of three cubes = 3 : 4 : 5
Let side of first cube = 3x
and side of second cube = 4x
and side of third cube = 5x
∴ Sum of volume of three cubes
= (3x)3 + (4x)3 + (5x)3
= 27x3 + 64x3 + 125x3 = 216x3
∴ Volume of the cube formed Jby melting these three cubes = 216x3
RD Sharma Class 9 Solutions Chapter 18 Surface Areas and Volume of a Cuboid and Cube VSAQS Q2.1
∴ Side of first cube = 3x = 3 x 2 = 6 cm
Side of second cube = 4x = 4×2 = 8 cm
and side of third cube = 5.r = 5 x 2 = 10 cm

Question 3.
If the perimeter of each face of a cube is 32 cm, find its lateral surface area. Note that four faces which meet the base of a cube are called its lateral faces.
Solution:
Perimeter of each face of a cube = 32 cm
∴ Length of edge = \(\frac { 32 }{ 4 }\) = 8 cm
and lateral surface area of the cube = 4 x (side)2
= 4 x 8 x 8 = 256 cm2

Question 4.
Find the edge of a cube whose surface area is 432 m2.
Solution:
RD Sharma Class 9 Solutions Chapter 18 Surface Areas and Volume of a Cuboid and Cube VSAQS Q4.1

Question 5.
A cuboid has total surface area of 372 cm2 and its lateral surface area is 180 cm2, find the area of its base.
Solution:
Total surface area of a cuboid = 372 cm2
and lateral surface area = 180 cm2
∴ Area of base and roof = 372 – 180 = 192 cm2
and area of base = \(\frac { 192 }{ 2 }\) = 96 cm2

Question 6.
Three cubes of each side 4 cm are joined end to end. Find the surface area of the resulting cuboid.
Solution:
By joining three cubes of side 4 cm each, end is end, we get a cuboid
Length of cuboid = 4 x 3 = 12 cm
Breadth = 4 cm
and height = 4 cm
RD Sharma Class 9 Solutions Chapter 18 Surface Areas and Volume of a Cuboid and Cube VSAQS Q6.1
∴ Surface area = 2(lb + bh + hl)
= 2[12 x4+4×4 + 4x 12] cm2
= 2[48 + 16 + 48] cm2
= 2 x 112 = 224 cm2

Question 7.
The surface area of a cuboid is 1300 cm2. If its breadth is 10 cm and height is 20 cm, find its length.
Solution:
Surface area of a cuboid = 1300 cm2
Breadth (b) = 10 cm
and height (h) = 20 cm
Let l be the length, then
= 2 (lb + bh + hl) = 1300
lb+ bh + hl = \(\frac { 1300 }{ 2 }\) = 650
l x 10 + 10 x 20 + 20 x l = 650
10l + 20l + 200 = 650
⇒ 30l = 650 – 200 = 450
⇒ l = \(\frac { 450 }{ 30 }\) = 15
∴ Length of cuboid = 15 cm

Hope given RD Sharma Class 9 Solutions Chapter 18 Surface Areas and Volume of a Cuboid and Cube VSAQS are helpful to complete your math homework.

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RD Sharma Class 9 Solutions Chapter 18 Surface Areas and Volume of a Cuboid and Cube Ex 18.2

RD Sharma Class 9 Solutions Chapter 18 Surface Areas and Volume of a Cuboid and Cube Ex 18.2

These Solutions are part of RD Sharma Class 9 Solutions. Here we have given RD Sharma Class 9 Solutions Chapter 18 Surface Areas and Volume of a Cuboid and Cube Ex 18.2

Other Exercises

Question 1.
A cuboidal water tank is 6 m long, 5 m wide and 4.5 m deep. How many litres of water can it hold? [NCERT]
Solution:
Length of water tank (l) = 6 m
Breadth (b) = 5 m
and depth (h) = 4.5 m
RD Sharma Class 9 Solutions Chapter 18 Surface Areas and Volume of a Cuboid and Cube Ex 18.2 Q1.1
∴ Volume of water in it = lbh
= 6 x 5 x 4.5 m3 = 135 m3
Capacity of water in litres = 135 x 1000 litres (1 m3 = 1000 l)
= 135000 litres

Question 2.
A cubical vessel is 10 m long and 8 m wide. How high must it be made to hold 380 cubic metres of a liquid? [NCERT]
Solution:
Length of vessal (l) = 10 m
Breadth (b) = 8 m
Volume = 380 m3
RD Sharma Class 9 Solutions Chapter 18 Surface Areas and Volume of a Cuboid and Cube Ex 18.2 Q2.1

Question 3.
Find the cost of digging a cuboidal pit 8 m long, 6 m broad and 3 m deep at the rate of ₹30 per m3. [NCERT]
Solution:
Length of pit (l) = 8m
Width (b) = 6 m
and depth (h) = 3 m
∴ Volume of earth digout = lbh
= 8 x 6 x 3 = 144 m3
Cost of digging the pit at the rate of ₹30 per m3
= 144 x 30 = ₹4320

Question 4.
If the areas of three adjacent faces of a cuboid are 8 cm2, 18 cm2 and 25 cm2. Find the volume of the cuboid.
Solution:
Let x, y, z be the three adjacent faces of the cuboid, then
x = 8 cm2, y = 18 cm2, z = 25 cm2
and let l, b, h are the dimensions of the cuboid, then
x = lb = 8 cm2
y = bh = 18 cm2
z = hl = 25 cm2
∴ Volume = lbh
RD Sharma Class 9 Solutions Chapter 18 Surface Areas and Volume of a Cuboid and Cube Ex 18.2 Q4.1

Question 5.
The breadth of a room is twice its height, one half of its length and the volume of the room is 512 cu. dm. Find its dimensions.
Solution:
Let breadth of a room (b) = x
RD Sharma Class 9 Solutions Chapter 18 Surface Areas and Volume of a Cuboid and Cube Ex 18.2 Q5.1

Question 6.
Three metal cubes with edges 6 cm, 8 cm and 10 cm respectively are melted together and formed into a single cube. Find the volume, surface area and diagonal of the new cube.
Solution:
Edge of first cube = 6 cm
Edge of second cube = 8 cm
and edge of third cube = 10 cm
∴ Volume of 3 cubes = (6)3 + (8)3 + (10)3 cm3
= 216 + 512 + 1000 cm3
= 1728 cm3
∴ Edge of so formed cube
RD Sharma Class 9 Solutions Chapter 18 Surface Areas and Volume of a Cuboid and Cube Ex 18.2 Q6.1

Question 7.
Two cubes, each of volume 512 cm3 are joined end to end. Find the surface area of the resulting cuboid.
Solution:
Volume of each volume = 512 cm3
∴ Side (edge) = \(\sqrt [ 3 ]{ 512 }\)
=\(\sqrt [ 3 ]{ { 8 }^{ 3 } }\)  = 8 cm
Now by joining two cubes, then Length of so formed cuboid (l)
= 8 + 8 = 16 cm
Breadth (b) = 8 cm
and height (h) = 8 cm
∴ Surface area = 2(lb + bh + hl)
= 2[16 x 8 + 8 x 8 + 8 x 16] cm2
= 2[128 + 64 + 128] cm2
= 2 x 320 = 640 cm2

Question 8.
A metal cube of edge 12 cm is melted and formed into three smaller cubes. If the edges of the two smaller cubes are 6 cm and 8 cm, find the edge of the third smaller cube.
Solution:
Edge of metal cube = 12 cm
∴ Its volume = (Edge)3 = (12)3 cm33
= 1728 cm3
It is melted and form 3 cubes
Edge of one smaller cube = 6 cm
and edge of second smaller cube = 8 cm
∴ Volume of two smaller cubes = (6)3 + (8)3 cm3
= 216 + 512 cm3 = 728 cm3
∴ Volume of third smaller cube = 1728 – 728 = 1000 cm3
∴ Edge of the third cube = \(\sqrt [ 3 ]{ 1000 }\)
= \(\sqrt [ 3 ]{ (10)3 }\)  cm = 10 cm

Question 9.
The dimensions of a cinema hall are 100 m, 50 m and 18 m. How many persons can sit in the hall, if each person requires 150 m3 of air?
Solution:
Length of cinema hall (l) = 100 m
Breadth (b) = 50 m
and height (h) = 18 m
∴ Volume of air in it = lbh
= 100 x 50 x 18 m= 90000 m3
Air required for one person = 150 m3
∴ Number of persons in the hall = \(\frac { 90000 }{ 150 }\) = 600 persons

Question 10.
Given that 1 cubic cm of marble weighs 0.25 kg, the weight of marble block 28 cm in width and 5 cm thick is 112 kg. Find the length of the block.
Solution:
Weight of 1 cm3 = 0.25 kg
Breadth of the block (b) = 28 cm
Thickness (h) = 5 cm
and total weight of the block = 112 kg
RD Sharma Class 9 Solutions Chapter 18 Surface Areas and Volume of a Cuboid and Cube Ex 18.2 Q10.1

Question 11.
A box with lid is made of 2 cm thick wood. Its external length, breadth and height are 25 cm, 18 cm and 15 cm respectively. How much cubic cm of a liquid can be placed in it? Also, find the volume of the wood used in it.
Solution:
Outer length of the closed wooden box (l) = 25 cm
Breadth (b) = 18 cm
and height (h) = 15 cm
Width of wood = 2 cm
RD Sharma Class 9 Solutions Chapter 18 Surface Areas and Volume of a Cuboid and Cube Ex 18.2 Q11.1
∴ Inner length = 25 – 2×2 = 25- 4 = 21cm
Breadth =18- 2×2 = 18-4 = 14 cm
and height =15- 2×2 = 15- 4=11 cm
Now outer volume = 25 x 18 x 15 cm3 = 6750 cm3
and inner volume = 21 x 14 x 11 cm3 = 3234 cm3
(i) Inner volume = 3234 cm3
(ii) Volume of wood = 6750 – 3234 = 3516 cm3

Question 12.
The external dimensions of a closed wooden box are 48 cm, 36 cm, 30 cm. The box is made of 1.5 cm thick wood. How many bricks of size 6 cm x 3 cm x 0.75 cm can be put in this box?
Solution:
External length of a closed wooden box (L) = 48 cm
Width (B) = 36 cm
and height (H) = 30 cm
Thickness of wood = 1.5 cm
RD Sharma Class 9 Solutions Chapter 18 Surface Areas and Volume of a Cuboid and Cube Ex 18.2 Q12.1
∴ Internal length (l) = 48 – 2 x 1.5 cm = 48 – 3 = 45 cm
Width (b) = 36 – 2 x 1.5 cm
= 36 – 3 = 33 cm
and height (h) = 30 – 2 x 1.5 cm
= 30 – 3 = 27 cm
Now volume of internal box
= lbh = 45 x 33 x 27 cm3
Volume of one bricks = 6 x 3 x 0.75 cm3
RD Sharma Class 9 Solutions Chapter 18 Surface Areas and Volume of a Cuboid and Cube Ex 18.2 Q12.2

Question 13.
A cube of 9 cm edge is immersed completely in a rectangular vessel containing water. If the dimensions of the base are 15 cm and 12 cm, find the rise in water level in the vessel.
Solution:
Edge of a cube = 9 cm
Volume of cube = (9)3 cm3
= 729 cm3
Now length of vessel (l) = 15 cm
and breadth (b) = 12 cm
RD Sharma Class 9 Solutions Chapter 18 Surface Areas and Volume of a Cuboid and Cube Ex 18.2 Q13.1

Question 14.
A field is 200 m long and 150 m broad. There is a plot, 50 m long and 40 m broad, near the field. The plot is dug 7 m deep and the earth taken out is spread evenly on the field. By how many metres is the level of the field raised? Give the answer to the second place of decimal.
Solution:
Length of a field (l) = 200 m
Breadth (b) = 150 m
Length of plot = 50 m
and breadth = 40 m
Depth of plot = 7 m
RD Sharma Class 9 Solutions Chapter 18 Surface Areas and Volume of a Cuboid and Cube Ex 18.2 Q14.1
RD Sharma Class 9 Solutions Chapter 18 Surface Areas and Volume of a Cuboid and Cube Ex 18.2 Q14.2

Question 15.
A field is in the form of a rectangle of length 18 m and width 15 m. A pit, 7.5 m long, 6 m broad and 0.8 m deep, is dug in a comer of the field and the earth taken out is spread- over the remaining area of the field. Find out the extent to which the level of the field has been raised.
Solution:
Length of a field (L) = 18m
and width (B) = 15 m
Length of pit (l) = 7.5 m
Breadth (b) = 6 m
and depth (h) = 0.8 m
RD Sharma Class 9 Solutions Chapter 18 Surface Areas and Volume of a Cuboid and Cube Ex 18.2 Q15.1
∴ Volume of earth dugout = lbh
= 7.5 x 6 x 0.8 m3
= 45 x 0.8 = \(\frac { 45 x 4 }{ 5 }\) = 36 m3
Total area of the field = L x B
= 18 x 15 = 270 m2
and area of pit = lb = 7.5 x 6 = 45 m2
∴ Remaining area of the field excluding pit
= 270 – 45 = 225 m2
Let by spreading the earth on the remaining part of the field, the height = h
= 225 x h = 36
⇒ h = \(\frac { 36 }{ 225 }\) = \(\frac { 4 }{ 25 }\)= 0.16 m = 16 cm
∴ Level of field raised = 16 cm

Question 16.
A village having a population of 4000 requires 150 litres of water per head per day. It has a tank measuring 20 m x 15m x 6 m. For how many days will the water of this tank last? [NCERT]
Solution:
Population of a village = 4000
Water required per head per day = 150 litres
∴ Total water required = 4000 x 150 litres = 600000 litres
Dimensions of a tank = 20mx 15mx6m
∴ Volume of tank = 20 x 15 x 6 m3 = 1800 m3
Capacity of water in litres = 1800 x 1000 litres (1 m3 = 1000 litres)
= 1800000 litres
The water will last for = \(\frac { 1800000 }{ 600000 }\) = 3 days

Question 17.
A child playing with building blocks, which are of the shape of the cubes, has built a structure as shown in the figure. If the edge of each cube is 3 cm, find the volume of the structure built by the child. [NCERT]
RD Sharma Class 9 Solutions Chapter 18 Surface Areas and Volume of a Cuboid and Cube Ex 18.2 Q17.1
Solution:
No. of cubes at the given structure = 1+ 2 + 3+ 4 + 5 = 15
Edge of one cube = 3 cm
∴ Volume of one cube = (3)3 = 3 x 3 x 3 cm3 = 27 cm3
∴Volume of the structure = 27 x 15 cm3 = 405 cm3

Question 18.
A godown measures 40 m x 25 m x 10 m. Find the maximum number of wooden crates each measuring 1.5 m x 1.25 m x 0.5 m that can be stored in the godown. [NCERT]
Solution:
Length of godown (L) = 40 m
Breadth (B) = 25 m
and height (H) = 10 m
∴ Volume of godown = LBH
= 40 x 25 x 10 = 10000 m3
Dimension of one wooden crates = 1.5 m x 1.25 m x 0.5 m
∴Volume of one crate = 1.5 x 1.25 x 0.5 m3 = 0.9375 m3
∴ Number of crates to be stored in the
RD Sharma Class 9 Solutions Chapter 18 Surface Areas and Volume of a Cuboid and Cube Ex 18.2 Q18.1

Question 19.
A wall of length 10 m was to be built across an open ground. The height of the wall is 4 m and thickness of the wall is 24 cm. If this wall is to be built up with bricks whose dimensions are 24 cm x 12 cm x 8 cm, how many bricks would be required? [NCERT]
Solution:
Length of wall (L) = 10 m = 1000 cm
Height (H) = 4 m = 400 cm
Thickness (B) = 24 cm = 24 cm
∴ Volume of wall = LBH = 1000 x 24 x 400 cm3 = 9600000 cm3
Dimensions of one brick = 24 cm x 12 cm x 8 cm = 2304 cm3
RD Sharma Class 9 Solutions Chapter 18 Surface Areas and Volume of a Cuboid and Cube Ex 18.2 Q19.1

Question 20.
If V is the volume of a cuboid of dimensions a, b, c and S is its surface area, then prove that
RD Sharma Class 9 Solutions Chapter 18 Surface Areas and Volume of a Cuboid and Cube Ex 18.2 Q20.1
Solution:
a, b, c are the dimensions of a cuboid S is the surface area and V is the volume
∴ V = abc and S = 2(lb + bc + ca)
RD Sharma Class 9 Solutions Chapter 18 Surface Areas and Volume of a Cuboid and Cube Ex 18.2 Q20.2

Question 21.
The areas of three adjacent faces of a cuboid are x, y and z. If the volume is V, prove that V= xyz.
Solution:
Let a, b, c are the dimensions of a cuboid then,
x = ab, y = bc, z = ca
and V = abc
Now L.H.S. = V2
= (abc)= a2b2c2
= ab.bc.ca = xyz = R.H.S.
Hence V2 = xyz

Question 22.
A river 3 m deep and 40 m wide is flowing at the rate of 2 km per hour. How much water will fall into the sea in a minute? [NCERT]
Solution:
Speed of water in a river = 2 km/hr
RD Sharma Class 9 Solutions Chapter 18 Surface Areas and Volume of a Cuboid and Cube Ex 18.2 Q22.1

Question 23.
Water in a canal 30 dm wide and 12 dm deep, is flowing with a velocity of 100 km per hour. How much area will it irrigate in 30 minutes if 8 cm of standing water is desired?
Solution:
Width of canal (b) = 30 dm = 3 m
Depth (h) = 12 dm = 1.2 m
Speed of water = 100 km/hr
Length of water flow in 30 minutes = \(\frac { 1 }{ 2 }\) hr
RD Sharma Class 9 Solutions Chapter 18 Surface Areas and Volume of a Cuboid and Cube Ex 18.2 Q23.1

Question 24.
Half cubic metre of gold-sheet is extended by hammering so as to cover an area of 1 hectare. Find the thickness of the gold- sheet.
Solution:
RD Sharma Class 9 Solutions Chapter 18 Surface Areas and Volume of a Cuboid and Cube Ex 18.2 Q24.1

Question 25.
How many cubic centimetres of iron are there in an open box whose external dimensions are 36 cm, 25 cm and 16.5 cm, the iron being 1.5 cm thick throughout? If 1 cubic cm of iron weighs 15 g, find the weight of the empty box in kg.
Solution:
External length of open box (L) = 36 cm
Breadth (B) = 25 cm
and Height (H) = 16.5 cm
Width of iron sheet used = 1.5 cm
∴ Inner length (l) = 36 – 1.5 x 2 = 36 – 3 = 33 cm
Breadth (b) = 25 – 2 x 1.5 = 25 – 3 = 22 cm
and Height (h) = 16.5 – 1.5 = 15 cm
∴ Volume of the iron used = Outer volume – Inner volume
= 36 x 25 x 16.5 – 33 x 22 x 15
= 14850 – 10890 = 3960 cm3
Weight of 1 cm3 = 15 g
RD Sharma Class 9 Solutions Chapter 18 Surface Areas and Volume of a Cuboid and Cube Ex 18.2 Q25.1

Question 26.
A rectangular container, whose base is a square of side 5 cm, stands on a horizontal table, and holds water upto 1 cm from the top. When a cube is placed in the water it is completely submerged, the water rises to the top and 2 cubic cm of water overflows. Calculate the volume of the cube and also the length of its edge.
Solution:
Base of the container = 5 cm x 5 cm
Level of water upto 1 cm from the top After placing a cube in it, the water rises to the top and 2 cubic cm of water overflows,
(i) ∴ Volume of water = 5 x 5 x 1 + 2 = 25 + 2 = 27 cm3
∴ Volume of cube = 27 cm3
RD Sharma Class 9 Solutions Chapter 18 Surface Areas and Volume of a Cuboid and Cube Ex 18.2 Q26.1

Question 27.
A rectangular tank is 80 m long and 25 m broad. Water-flows into it through a pipe whose cross-section is 25 cm2, at the rate of 16 km per hour. How much the level of the water rises in the tank in 45 minutes.
Solution:
Length of tank (l) = 80 m
Breadth (b) = 25 m
Area of cross section of the month of pipe = 25 cm2
and speed of water-flow =16 km/h
∴ Volume of water is 45 minutes
RD Sharma Class 9 Solutions Chapter 18 Surface Areas and Volume of a Cuboid and Cube Ex 18.2 Q27.1

Question 28.
Water in a rectangular reservoir having base 80 m by 60 m is 6.5 m deep. In what time can the water be emptied by a pipe of which the cross-section is a square of side 20 cm, if the water runs through the pipe at the rate of 15 km/hr.
Solution:
Length of reservoir (l) = 80 m
Breadth (b) = 60 m
and depth (h) = 6.5 m
∴ Volume of water in it = lbh = 80 x 60 x 6.5 m3 = 31200 m3
Area of cross-section of the month of pipe = 20 x 20 = 400 cm2
RD Sharma Class 9 Solutions Chapter 18 Surface Areas and Volume of a Cuboid and Cube Ex 18.2 Q28.1

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NCERT Exemplar Solutions for Class 9 Science Chapter 10 Gravitation


NCERT Exemplar Solutions for Class 9 Science Chapter 10 Gravitation

These Solutions are part of NCERT Exemplar Solutions for Class 9 Science . Here we have given NCERT Exemplar Solutions for Class 9 Science Chapter 10 Gravitation

MULTIPLE CHOICE QUESTIONS

Question 1.
Two objects of different masses falling freely near the surface of moon would
(a) have same velocities at any instant
(b) have different accelerations
(c) experience forces of same magnitude
(d) undergo a change in their inertia.
Answer:
(a) Explanation : During free fall, acceleration remains the same irrespective of the mass of the object. Force is directly proportional to the mass of a freely falling object.

More Resources

Question 2.
The value of acceleration due to gravity
(a) is same on equator and poles
(b) is least on poles
(c) is least on equator
(d) increases from pole to equator.
Answer:
(c) Explanation :
NCERT Exemplar Solutions for Class 9 Science Chapter 10 Gravitation image - 14
Equatorial radius (R) is more than the polar radius.

Question 3.
The gravitational force between two objects is F. If masses of both objects are halved without changing distance between them, then the gravitation force would become
(a) F/4
(b) F/2
(c) F
(d) 2F
Answer:
NCERT Exemplar Solutions for Class 9 Science Chapter 10 Gravitation image - 1

Question 4.
A boy is whirling a stone tied with a string in an horizontal circular path the string breaks, the stone
(a) will continue to move in the circular path
(b) will move along a straight line towards the centre of the circular path
(c) will move along a straight line tangential to the circular path
(d) will move along a straight line perpendicular to the circular path away from the boy.
Answer:
(c) Explanation : Due to inertia of directions.

Question 5.
In the relation F = G M m/d, the quantity G
(a) depends on the value of g at the place of observation
(b) is used only when the earth is one of the two masses
(c) is greatest at the surface of the earth
(d) is universal constant of nature.
Answer:
(d) Explanation : The value of ‘G’ is same throughout the universe.

Question 6.
Law of gravitation gives the gravitational force between
(a) the earth and a point mass only
(b) the earth and sun only
(c) any two bodies having some mass
(d) two charged bodies only.
Answer:
NCERT Exemplar Solutions for Class 9 Science Chapter 10 Gravitation image - 2

Question 7.
The value of quantity G in the law of gravitation
(a) depends on mass of earth only
(b) depends on radius of earth only
(c) depends on both mass and radius of earth
(d) is independent of mass and radius of the earth.
Answer:
(d) Explanation : G is universal constant.

Question 8.
Two particles are placed at some distance. If the mass of each of the two particles is doubled, keeping the distance between them unchanged, the value of gravitational force between them will be
(a) 1/4 times
(b) 4 times
(c) 1/2 times
(d) unchanged.
Answer:
NCERT Exemplar Solutions for Class 9 Science Chapter 10 Gravitation image - 3

Question 9.
The atmosphere is held to the earth by
(a) gravity
(b) wind
(c) clouds
(d) earths magnetic field.
Answer:
(a).

Question 10.
The force of attraction between two unit point masses separated by a unit distance is called
(a) gravitational potential
(b) acceleration due to gravity
(c) gravitational field
(d) universal gravitational constant.
Answer:
NCERT Exemplar Solutions for Class 9 Science Chapter 10 Gravitation image - 4

Question 11.
The weight of an object at the centre of the earth of radius R is
(a) zero
(b) infinite
(c) R times the weight at the surface of the earth
(d) 1/R2 times the weight at surface of the earth.
Answer:
(a) Explanation : W = mg. The value of ‘g’ at the centre of earth is zero.

Question 12.
An apple falls from a tree because of gravitational attraction between the earth and apple. If F1 is the magnitude of force exerted by the earth on the apple and F2 is the magnitude of force exerted by apple on earth, then
(a) F1 is very much greater than F2
(b) F2 is very much greater than F1
(c) F1 is only a little greater than F2
(d) F1 and F2 are equal.
Answer:
NCERT Exemplar Solutions for Class 9 Science Chapter 10 Gravitation image - 5

SHORT ANSWER Of QUESTIONS

Question 13.
What is the source of centripetal force that a planet requires to revolve around the sun ? On what factors does that force depend ?
Answer:
The source of centripetal force that a planet requires to revolve around the sun is the gravitational force between the sun and the planet. Thus,
NCERT Exemplar Solutions for Class 9 Science Chapter 10 Gravitation image - 6
where m is the mass of the sun, is the mass of the planet and r is the distance between the sun and the planet.
Thus, the force depends upon

  1. the mass of the sun,
  2. the mass of the planet and
  3. the distance between the sun and the planet.

Question 14.
On the earth, a stone is thrown from a height in a direction parallel to the earths surface while another stone is simultaneously dropped from the same height. Which stone would reach the ground first and why ?
Answer:
Both stones will reach the ground simultaneously. Initial velocity of both the stones in the downward direction is zero and the acceleration of both the stones in the downward direction is same and equal to g.
NCERT Exemplar Solutions for Class 9 Science Chapter 10 Gravitation image - 7
so both stones take same time to reach the ground.

Question 15.
Suppose gravity of earth suddenly becomes zero, then in which direction will the moon begin to move if no other celestial body affects it ?
Answer:
Gravity of earth provides necessary centripetal force to the moon to move in a circular path around the earth. If gravity becomes zero, there is no centripetal force and hence, the moon will begin to move in a straight line along to the tangent at the point on the circular path due to inertia of direction.

Question 16.
Identical packets are dropped from two aeroplanes. One above the equator and the other above the north pole both at height h. Assuming all conditions are identical will those packets take same time to reach the surface of earth. Justify your answer.
(CBSE Sample Paper)
Answer:
Time taken by an object to fall through height h at a place is given by
NCERT Exemplar Solutions for Class 9 Science Chapter 10 Gravitation image - 8
Since, value of ‘g’ at poles is greater than at the equator, therefore, packet dropped above the north pole will take less time than the packet dropped above the equator to reach the surface of the earth.

Question 17.
The weight of any person on the moon is about 1/6 times that on the earth. He can lift a mass of 15 kg on the earth. Whatwill be the maximum mass, which can be lifted by the same force applied by the person on the moon ? (CBSE Sample Paper)
Answer:
NCERT Exemplar Solutions for Class 9 Science Chapter 10 Gravitation image - 9

Question 18.
Calculate the average density of earth in terms of g, G,m?
Answer:
NCERT Exemplar Solutions for Class 9 Science Chapter 10 Gravitation image - 10

Question 19.
The earth is acted upon by gravitation of sun, even though it does not fall into the sun. Why ? (CBSE 2012)
Answer:
The earth revolves around the sun. The centripetal force is needed by the earth to revolve around the sun. This centripetal force is provided by the gravitational force between the sun and the earth. The earth keeps on moving around the sun as long as gravitational force between the earth and the sun acts on it.

Question 20.
How does the weight of an object vary with respect to mass and radius of the earth. In a hypothetical case, if the diameter of the earth becomes half of its present value and its mass becomes four times of its present value, then how would the weight of any object on the surface of the earth be affected ? (CBSE 2012)
Answer:
NCERT Exemplar Solutions for Class 9 Science Chapter 10 Gravitation image - 11

Question 21.
How does the force of attraction between two bodies depend upon their masses and distance between them ? A student thought that two bricks tied together would fall faster than a single one under the action of gravity. Do you agree with this hypothesis or not ? Comment.
Answer:
The force of attraction between two bodies of masses m1 and m2 and separated by a distance r is given by
NCERT Exemplar Solutions for Class 9 Science Chapter 10 Gravitation image - 12
This force is known as gravitational force. The gravitational force is

  1. directly proportional to the product of the masses of two bodies and
  2. inversely proportional to the square of the distance between them.

The hypothesis is not correct. This is because, all bodies in the absence of any force of friction fall with the same acceleration (known as acceleration due to gravity) irrespective of their masses. Hence two bricks tied together will not fall faster than a single brick under the action of gravity.

Question 22.
Two objects of masses m1 and mhaving the same size are dropped simultaneously from heights h1 and h2– respectively. Find out the ratio of time they would take in reaching the ground. Will this ratio remain the same if

  1. one of the object is hollow and the other one is solid and
  2. both of them are hollow, size remaining the same in each case. Give reason.

Answer:
NCERT Exemplar Solutions for Class 9 Science Chapter 10 Gravitation image - 13
Ratio will be same as it does not depend on the mass and size of objects.

Hope given NCERT Exemplar Solutions for Class 9 Science Chapter 10 Gravitation are helpful to complete your science homework.

If you have any doubts, please comment below. Learn Insta try to provide online science tutoring for you.