# Gravitation

## NCERT Solution

### Part 1

Question 1: How does the force of gravitation between two objects change when the distance between them is reduced to half?

**Answer:** The force of gravitation varies inversely as square of the distance between two objects.

`F ∝ 1/d^2`

When all other factors remain constant, and distance is 1 unit then;

`F = 1/1^2 = 1`

When distance is ½ unit then;

`F = 1/(1/2)^2`

Or, `F = 4`

This means that the force of gravitation between two objects becomes four times when the distance between them is reduced to half.

Question 2: Gravitational force acts on all objects in proportion to their masses. Why then, a heavy object does not fall faster than a light object?

**Answer:** All objects fall on the earth due to acceleration due to gravity. The value of g is constant at a given place. Hence, irrespective of their masses, all objects fall at the same rate.

Question 3: 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 × 10^{24} kg and radius of the earth is 6.4 × 10^{6} m.)

**Answer:** Given; mass of object = 1 kg

Mass of earth `= 6 xx 10^24`

Radius of earth `= 6.4 xx 10^6`

`G = 6.67 xx 10^-11`

Gravitational force between the earth and the object can be calculated as follows:

`F=G(Mm)/(R^2)`

`=6.67xx10^-11xx(6xx10^24\xx1)/(6.4xx10^6)^2`

`=(6.67xx6xx10^13)/(6.4xx6.4xx10^12)`

`=0.97xx10=9.8N`

Question 4: 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?

**Answer:** The force of attraction between two objects depends on product of masses of the two objects. Hence, the force of attraction between two objects is constant for a given distance between them. So, both the earth and the moon would attract each other with equal force.

Question 5: If the moon attracts the earth, why does the earth not move towards the moon?

**Answer:** The force of attraction between the earth and the moon is constant. Mass of the earth is greater than the mass of the moon. Due to greater mass, the earth accelerates at a faster rate than moon. Due to this, the earth does not move towards the moon.

Question 6: What happens to the force between two objects, if

(a) the mass of one object is doubled?

**Answer:** F ∝ Mm

If mass of one object is doubled then;

`F ∝ 2Mm`

This means the force will become double.

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

**Answer:** `F ∝ 1/d^2`

If distance is doubled then;

`F ∝ 1/4d`

This means the force becomes four times.

If distance is tripled then;

`F ∝ 1/9d`

This means the force becomes nine times.

(c) the masses of both objects are doubled?

**Answer:** `F ∝ Mm`

If masses of both objects are doubled then;

`F ∝ 2M2m`

Or, `F ∝ 4Mm`

This means the force becomes four times.

Question 7: What is the importance of universal law of gravitation?

**Answer:** The universal law of gravitation helps in explaining many phenomena. Some of them are as follows:

- We keep on remaining on the earth’s surface.
- The earth moves around the sun.
- The planets and their satellites remain in their respective orbits.
- The tides happen at regular intervals.

Question 8: What is the acceleration of free fall?

**Answer:** When a body is in free fall, the acceleration it undergoes is called acceleration of free fall. It is same as acceleration due to gravity. The value of g is 9.8 m/s^{2}.

Question 9: What do we call the gravitational force between the earth and an object?

**Answer:** Weight of the object

Question 10: Amit buys few grams of gold at the poles as 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? [Hint: The value of g is greater at the poles than at the equator.]

**Answer:** Since the value of g is greater at the poles than at the equator, the weight of gold at the poles is more than the weight at the equator. So, Amit’s friend will not agree with the weight of gold bought.

Question 11: Why will a sheet of paper fall slower than one that is crumpled into a ball?

**Answer:** A sheet of paper will experience greater air resistance than the crumpled ball of paper; while falling. So, the sheet of paper will fall slower than the crumpled ball of paper.

Question 12: 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?

**Answer:** Weight of an object on earth can be calculated as follows:

`W = m xx g`

`= 10 xx 9.8 = 98 N`

Weight of the same object on moon is 1/6th its weight on earth:

Weight on moon `= 98/6 = 16.33 N`

Question 13: A ball is thrown vertically upwards with a velocity of 49 m/s. Calculate

(a) the maximum height to which it rises,

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

**Answer:** This can be calculated by using the following equation of motion:

`v^2-u^2= 2gs`

where; u = initial velocity, v = final velocity, g = acceleration due to gravity and s = distance.

In this case, final velocity v = 0 because the object will come to rest on reaching the maximum height.

Or, `0 - 49^2 = 2 xx -9.8 xx s`

Or, `2401 = 19.6 xx s`

Or, `s = 2401/19.6 = 122.5 m`

The time taken to reach the maximum height can be calculated as follows:

`v = u + gxxt`

Or, `49 = 0 + 9.8 xx t`

Or, `t = 49/9.8 = 5 s`

Now, time of ascent = time of descent

So, total time to return to the surface of the earth `= 5 + 5 = 10 s`