Gravitation NCERT Solution, study material, CBSE Notes

NCERT Solution: Gravitation

Why does an object float or sink when placed on the surface of water?

→ An object sink in water if its density is greater than that of water.
→ An object floats in water if its density is less than that of water.

You find your mass to be 42 kg on a weighing machine. Is your mass more or less than 42 kg?

When we weigh our body, an upward force acts on it. This upward force is the buoyant force. As a result, the body gets pushed slightly upwards, causing the weighing machine to show a reading less than the actual value.

You have a bag of cotton and an iron bar, each indicating a mass of 100 kg when measured on a weighing machine. In reality, one is heavier than other. Can you say which one is heavier and why?

The cotton bag is heavier than the iron bar. The cotton bag experiences larger up thrust of air than the iron bar. So, the weighing machine indicates a smaller mass for cotton bag than its actual mass.

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

According to the universal law of gravitation, gravitational force (F) acting between two objects is inversely proportional to the square of the distance (r) between them, i.e.,

If distance r becomes r/2, then the gravitational force will be proportional to

Hence, if the distance is reduced to half, then the gravitational force becomes four times larger than the previous value./p>

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

All objects fall on ground with constant acceleration, called acceleration due to gravity (in the absence of air resistances). It is constant and does not depend upon the mass of an object. Hence, heavy objects do not fall faster than light objects.

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 × 10²⁴kg and radius of the earth is 6.4 × 10⁶ m).

According to the universal law of gravitation, gravitational force exerted on an object of mass m is given by:

Where,

Mass of Earth, M = 6 x 10²⁴kg

Mass of object, m = 1 kg

Universal gravitational constant, G = 6.7 x 10 ^{- 11}Nm2kg ^{- 2}

Since the object is on the surface of the Earth, r = radius of the Earth (R)

r= R = 6.4 x 10⁶ m

Gravitational force,

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?

According to the universal law of gravitation, two objects attract each other with equal force, but in opposite directions. The Earth attracts the moon with an equal force with which the moon attracts the earth.

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

The Earth and the moon experience equal gravitational forces from each other. However, the mass of the Earth is much larger than the mass of the moon. Hence, it accelerates at a rate lesser than the acceleration rate of the moon towards the Earth. For this reason, the Earth does not move towards the moon.