Gravitation-NCERT Solutions

Class IX Science
NCERT Solutions for Gravitation

NCERT TEXTBOOK PAGE 134

Q1. State the universal law of gravitation.

Ans. Every object in the universe attracts every other object with a force which is proportional to the product of their masses and inversely proportional to the square of the distance between them. The force is along the line joining the centres of two objects

Q2. Write the formula to find the magnitude of the gravitational force between the earth and an object on the surface of the earth.

Ans. The gravitational force between the earth and an object on its surface

M_e = Mass of the earth

NCERT TEXTBOOK PAGE 136

Q1. What do you mean by free fall?

Ans. Whenever an object falls toward earth under the force of gravity one and no other force is present, the motion of object is said to be “free fall”.

Q2. What do you mean by acceleration due to gravity?

Ans. The acceleration of free fall is the acceleration due to gravity. We can also say the acceleration of an object due to gravitational force of earth acting on it is known as acceleration due to gravity.

NCERT TEXTBOOK PAGE 138

Q1. What are the differences between the mass of an object and its weight?

Ans.

Mass	Weight
1. Mass of a body is the measure of its inertia.	1. Weight of the body is the force with which it is attracted towards the earth (W = m x g).
2. Its S.I. unit is kg.	2. Its S.I unit is Newton.
3. It remains constant everywhere and it cannot be zero.	3. Its value changes from place to place and it can be zero.
4. It can be measured by beam-balance.	4. It can be measured by spring balance.
5. It has only magnitude i.e. it is a scalar quantity.	5. It has both magnitude and direction i.e.

Q2. Why is the weight of an object on the moon 1/6th its weight on the earth?

Ans. The weight of an object� depends on ‘g’ acceleration due to gravity, and the value of ‘g’ on earth: and moon is not same.

The mass and radius of the earth is more than the mass and radius of the moon.

the weight of a body on the earth is 6 times more than the weight of a same body on moon.

QUESTIONS FROM NCERT TEXTBOOK

Q1. How does the force of gravitation between two objects change when the distance between them is reduced to half?

Ans.

The force of gravitation becomes 4 times more.

Q2. Gravitational force acts on all objects in proportion to their masses. Why then, a heavy object does not fall faster than a light object?

Ans. The heavy object when falls, the acceleration due to gravity ‘g’ is acting which is independent of the mass of the body.

Gravitation force is

∴ F and g are different.

Q3. What is the magnitude of the gravitational force between the earth and a 1 kg object on its surface?

[Mass of the earth is 6 x 10²⁴ kg and radius of the earth is 6.4 x 10⁶ m].

Ans. The magnitude of the gravitational force between earth and an object is given by the formula.

Q4. The earth and the moon are attracted to each other by gravitational force. Does the earth attract the moon with a force that is greater or smaller or the same as the force with which the moon attracts the earth? Why?

Ans. The value of F is same for earth and the moon. Both bodies will exert the same amount of force on each other.

As per universal law of gravitation, every body attracts the other body with some force and this force is same for both the bodies called gravitational force.

Q5. If the moon attracts the earth, why does the earth not move towards; the moon?

Ans. According to the universal, law of gravitation both moon and earth attract each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of distance between them.

The force of attraction of moon’ on the earth is present, but the earth does not appear to move towards the moon as the mass of the earth is large and the distance between the moon and earth is so large, even if the earth is attracted/moves towards the ,moon it is negligible, cannot be seem.

Q6. What: happens to the force between two objects, if

(i) the mass of one object is doubled?

(ii) the distance between the objects is doubled and tripled?

(iii) the masses of both objects are doubled?

Ans. (i) If the mass of one object is doubled, the force between two objects will be doubled (increases)

(ii) If the distance been the objects is doubled the force between two objects will be one-fourth and if the distance will be tripled, the force will be one-ninth (1/9).

(iii) If the masses of both objects are doubled the force will be 4 times.

Q7. What is the importance of universal law of gravitation?

Ans. The universal law of gravitation explains several phenomena:

(i) it explains about the force that binds the earth,

(ii) the motion of the moon around the earth,

(iii) the motion of planets around the sun, and

(iv) the tides due to the moon and the sun.

Q8. What is the acceleration-of free fall?

Ans. The acceleration of free fall is; when the Body falls due to earth’s gravitational pull, its velocity changes and is said to be accelerated due to .the earth’s gravity and it falls freely called as free fall. This acceleration is calculated to be 9.8 m/s².

Q9. What do we call the gravitational force between the earth and an object?

Ans. The gravitational force between the earth and an object is called force due to gravity.

Q10. Amit buys few grams of gold at the poles per the instruction of one of his friends. He hands over the same when he meets him at the equator. Will the friend agree with the weight of gold bought? If not, why?

[Hints: The value of g is greater at the poles than at the equator.]

Ans. Weight of the body is given by the formula

W = mg

It depends ors the value of ‘g’ i.e., acceleration due to gravity.

The weight of gold at poles = W_p = m × g (poles)

Value of g at poles is more than the value of g at equator.

The weight of gold at equator = W_e = m × g (equator)

∴ W_p > W_e.

The weight at pole of the same gold is found to be more as compared to the weight at the equator.

Q11. Why will a sheet of paper fall slower than one that is crumpled into a ball?

Ans. A sheet of paper has larger surface area and while falling down it has to overcome the force exerted by air/wind. current, called as air resistance.

The crumpled paper has smaller surface area and it has to overcome very less amount of air current.

Q12. Gravitational force on the surface of the moon is only 1/6 as strong as gravitational force on the earth. What is the weight in Newtons of a 10 kg object on the moon and on the earth?

Ans. Mass of the object = 10 kg

Weight of the object on earth = W = m × g

∴ W = 10 × 9.8

W = 98 N

Weight of the object on moon =

th the weight on the earth.

As the gravitational force on the surface of the moon is only

th as strong as gravitational force on the surface of the earth.

∴ Weight of the object on moon

Weight on earth = 98 N

Weight on moon = 16.3 N

Q13. A ball is thrown vertically upwards with a velocity of 49 m/s. Calculate

(i) the maximum height to which it rises,

(ii) the total time it takes to return to the surface of the earth.

Ans. (i) Initial velocity = 49 m/s

Final velocity = 0 m/s

a = g = –9.8 m/s²

Height = Distance = s = ?

∴ v² – u² = 2gs

0² – (49)² = 2 (–9.8) × s

(ii) Time take t = ?

v = u + gt

∴ 0 = 49 + (–9.8) × t

Total time taken to return the surface of the earth by the ball is 5 s + 5 s = 10 s.

Q14. A stone is released from the top of a tower of height 19.6 m. Calculate its final velocity just before touching the ground?

Ans. Data u = 0 m/s

v = ?

h = s = 19.6 m

g = 9.8 m/s² (falling down)

v² – u² = 2gs

v² – (0)² = 2 x 9.8 x 19.6

v = 19.6 m/s

The final velocity just before touching the ground is 19.6 m/s.

Q15. A stone is thrown vertically upward with an initial velocity of 40 m/s. Taking g = 10 m/s², find the maximum height reached by the stone. What is the net displacement and the total distance covered by the stone?

Ans. u = 40 m/s

g = –10 m/s² (going against gravity)

h = s = ?

v = 0

v² – u² = 2gs

(0)² – (40)² = 2 (–10) x s

Net displacement of the stone = 0 (As the stone falls, back to the same point.)

Total distance covered by stone = 80 m + 80 m

(up) (down)

= 160 m

Q16. Calculate the force of gravitation between the earth and the Sun, given that the mass of the earth = 6 x 10²⁴ kg and of the Sun = 2 x 10³⁰ kg. The average distance between the two is 1.5 x 10¹¹m.

Ans. Me = 6 x 10²⁴ kg G = 6.67 x 10^–11 Nm²/kg²

Ms = 2 x 10³⁰ kg

d = 1.5 x 10¹¹ m

Q17. A stone is allowed to fall from the top of a tower 100 m high and at the same time another stone is projected vetically upwards from the ground with a velocity of 25 m/s. Calculate when and where the two stones will meet.

Ans. h = 100 m

time t = ? g = 10 m/s²

Height covered by the falling stone = s¹