A ball is dropped from a spacecraft revolving around the earth at a height of 120 km. What will happen to the ball

The correct option is: It will continue to move with velocity v along the original orbit of spacecraft.

To understand why this happens, let us break down the physical principles involved step-by-step:

1. Initial State of the Ball and Spacecraft:
Before being dropped, the ball is inside the spacecraft, which is revolving around the Earth at a height of 120 km. Both the spacecraft and the ball are moving together with an orbital velocity $v$ relative to the Earth. At this height, the gravitational pull of the Earth provides the necessary centripetal force required to keep them in their circular orbit.

2. Effect of "Dropping" the Ball:
When the ball is released or "dropped" from the spacecraft, it is not given any push or force towards the Earth or in any other direction relative to the spacecraft. It is simply let go. According to Newton's first law of motion (the law of inertia), an object in motion will continue to stay in its state of motion unless acted upon by an external unbalanced force.

3. Forces Acting on the Ball:
Once released, the only significant force acting on the ball is the gravitational force of the Earth. At a height of 120 km, the acceleration due to gravity is virtually the same for both the spacecraft and the ball. Since both experience the same gravitational acceleration and start with the same orbital velocity $v$, they will both follow the exact same path.

Conclusion:
Because of inertia and the gravitational force acting as a centripetal force, the ball does not fall to the Earth or fly away into deep space. Instead, it continues to revolve around the Earth in the same orbit, keeping pace with the spacecraft with the same velocity $v$.