Chapter 11: GRAVITATION

Chapter 11: Gravitation Class 10 Science and Technology (212) NIOS Textbook Solutions

Chapter 11. GRAVITATION

INTEXT QUESTIONS 11.1

1. Why do two students sitting close to each other not feel force of gravitational attraction between them?

Answer: Gravitational force is extremely weak. Therefore, small masses do not attract each other due to this force.

2. Distance between two bodies is increased by a factor of four. How much will be the change in the force of gravitation?

Answer: As the force of gravitation is inversely proportional to the square of the distance between two bodies, the force will decrease by a factor of 1/16.

3. Why is G known as universal gravitational constant?

Answer: The value of G is same everywhere on the earth or in the universe. Therefore, G is known as universal gravitational constant.

INTEXT QUESTIONS 11.2

1. What do you mean by acceleration due to gravity?

Answer: The acceleration produced due to force of attraction by the earth is known as acceleration due to gravity.

2. Why do a heavier and a lighter object when dropped from a same height fall at the same rate?

Answer: Because the acceleration due to gravity is same for both heavy and light objects.

3. State SI unit of acceleration due to gravity.

Answer:  SI unit for acceleration due to gravity is m/s² .

4. Write equations of motion of an object moving under gravity.

Answer: The equations of motion for an object moving under gravity are:

(i) v=u+at

(ii) s=ut+12gt2

(iii) v²=u²+2gs

Where, u = initial velocity, v = final velocity, s = displacement , t = time, and g = acceleration due to gravity.

INTEXT QUESTIONS 11.3

1. Write two differences between mass of an object and its weight.

Answer: The two differences between mass of an object and its weight are :

Mass	Weight
Mass is the amount of matter present in an object.	Weight is the gravitational force acting on an object.
Mass remains constant everywhere.	Weight changes from place to place depending on gravity.

2. State two factors on which weight of an object depends.

Answer: Weight of an object depends upon

(a) mass of the body

(b) acceleration due to gravity.

3. What will be the weight of an apple while it is falling from a tree?

Answer: While an apple is falling from a tree, its apparent weight becomes zero because the apple and the Earth move together under the action of gravity.

INTEXT QUESTIONS 11.4

1. Hold a mug full of water inside a bucket filled with water. Now lift it above the surface of water. Why do you feel it is heavier now?

Answer: When immersed in water a buoyant force acts on the mug. Therefore, it feels lighter inside water. When lifted above the surface of water it feels heavier.

2. Why does a piece of cork released under water bounce back?

Answer: A piece of cork released under water bounces back because the upthrust (buoyant force) exerted by water on the cork is greater than its weight. Hence, the cork rises and comes back to the surface.

3. What do you mean by buoyant force?

Answer: When an object is immersed in a fluid it experiences an upward force which is known as buoyant force.

4. Does the buoyant force act on a body when it is kept in vacuum?

Answer: No, buoyant force does not act on a body kept in vacuum because buoyant force is produced by a fluid and there is no fluid in vacuum.

5. State two applications of Archimedes’ principle.

Answer: Applications of Archimedes’s principle:

(i) In designing ships and submarines

(ii) Hydrometers or lactometers.

TERMINAL EXERCISE

1. State Newton’s law of gravitation.

Answer: Newton’s law of gravitation states that, every particle in the universe attracts every other particle with a force, which is proportional to the product of their masses and inversely proportional to the square of the distance between them.

2. How does the force of gravitation between two objects change when the distance between them is doubled?

Answer: According to the law of gravitation, the gravitational force between two objects is

F=G Mmr2

Where, F = gravitational force  , G = universal gravitational constant , M and m are the masses of the two objects  , r = distance between their centres

When the distance is doubled, i.e., r'=2r

F'=G Mmr'2=G Mm(2r)²=14×GMmr²=14×F=F4

3. How does the gravitational force between two objects change if the masses of both objects are doubled?

Answer: According to the law of gravitation, the gravitational force between two objects is

F=G Mmr2

Where, F = gravitational force  , G = universal gravitational constant , M and m are the masses of the two objects  , r = distance between their centres

When the masses of both objects are doubled,  i.e., M'=2M  and  m'=2m 

F'=G M'm'r2=G (2M)(2m)r²=4GMmr²=4×GMmr²=4 F 

4. Derive an expression for the acceleration due to gravity on the surface of the earth in terms of earth’s mass, gravitational constant and radius of earth.

Answer: According to the Universal Law of Gravitation, the gravitational force F exerted by the Earth on the object is:

F=GMmr² …………(i)

Where,  G = gravitational constant , M = mass of the Earth , m = mass of the object and r = radius of the Earth (distance between the centers)

According to Newton's second law, the force acting on the object is also given by

 F=m⋅g…………ii

Where g is the acceleration due to gravity.

From (i) and (ii) , we get

mg=GMmr2

⇒g=GMr2

5. Write the equations of motion of an object moving or falling only under gravity.

Answer: The equations are:

(i)  v=u+gt

(ii)  s=ut+12gt²  

(iii)  v²=u²+2gs  

Where, u = initial velocity  , v = final velocity , g = acceleration due to gravity, t = time taken and s = distance covered .

6. What are the differences between the mass of an object and its weight? On what factors does the weight of an object depend?

Answer: The difference between Mass and Weight :

Mass	Weight
Mass is the amount of matter present in an object.	Weight is the gravitational force acting on an object.
SI unit is kilogram (kg).	SI unit is newton (N).
Mass remains the same everywhere.	Weight changes from place to place depending on gravity.
Measured using a beam balance.	Measured using a spring balance.

Weight of an object depends on:

(i) Mass of the object

(ii) Acceleration due to gravity

7. Why does a capped empty plastic bottle released under water bounces back to the surface of water?

Answer: A capped empty plastic bottle released under water rises back to the surface because the buoyant force of water acting upward is greater than the weight of the bottle.

8. What is force of buoyancy? What are the factors on which the magnitude of the buoyant force acting on a body at a given place depends?

Answer: Buoyant force is the upward force exerted by a fluid on an immersed body.

Its magnitude depends on the density of the fluid and the volume of fluid displaced by the body.

9. State Archimedes’ principle. Give two applications of Archimedes’ principle.

Answer: Archimedes’ principle states that, when a body is immersed fully or partially in a fluid, it experiences an upward force that is equal to the weight of the fluid displaced by it.

Two applications of Archimedes’ principle are:

(i) Hydrometers are used to determine the density of liquids.

(ii) Lactometers are used to determine the purity of milk.

10. If the average distance between the earth and the sun is 1.5×1011  m, calculate the force of gravitation between the two. Given:

mass of the earth = 6×1024 kg

mass of the sun =2×1030 kg

value of G=6.7×10-11Nm²kg-2  

Answer:  Given, m = 6×1024 kg , M =2×1030 kg ,  G=6.7×10-11Nm²kg-2  and r =1.5×1011  m

The force exerted by the earth on the moon is   

11. What is the mass of an object whose weight is 49N? (Given g = 9.8 m/s² ).

Answer:  Here, W = 49 N and g = 9.8 m/s²

We have,

W=mg

⇒m=Wg=499.8

⇒m=5 kg 

Therefore, the mass of the object is 5 kg.

12. A stone is dropped from the top of a tower 45 m high. What is its velocity when it hits the ground? (Given g = 10 m/s²).

Answer: Here, s=45 m ,  u=0 m/s ,  g=10 m/s² and  v= ?

We have,

v2=u2+2gs

⇒v2=0+2×10×45=900

⇒v2=900=(30)²

⇒v=30 m/s

The velocity of the stone when it hits the ground is 30 m/s downward.

13. A body weighs 3.5 N in air and 2 N in water. How much buoyant force acts on the body ?

Answer: Given, Weight of body in air = 3.5 N  and Weight of body in water = 2 N

Buoyant Force = Weight in air – Weight in water = 3.5 – 2 = 1.5 N

Therefore, the buoyant force acting on the body is 1.5 N.

14. A body is immersed in a liquid. If the liquid displaced by the body weighs 1 N then what is the buoyant force acting on the body?

Answer: According to Archimedes' principle, the buoyant force acting on a body immersed in a liquid is equal to the weight of the liquid displaced by it. Therefore, the buoyant force = 1 N.

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