Question

A stone is released from an elevator going up with an acceleration $a$ and speed $u$. The acceleration and speed of the stone just after the release is:
A) $a$ upwards, zero
B) $(g - a)$ upwards, $u$ downwards
C) $(g - a)$ downwards, zero
D) $g$ downwards, $u$ upwards

Answer 1

Hint: In order to find the acceleration and speed of the stone after the release, we need to analyse the directions of the initial velocity, acceleration and the force along with acceleration due to gravity acting on the stone.

Complete step by step solution:
In the question, it is given that the elevator is going upwards. The acceleration of the elevator is $a$ and the speed of the elevator is $u$. Thus the stone will have the same acceleration and speed of the elevator just before it is released from the elevator.
That is, Acceleration of the stone = $a$
Speed of the stone = $u$
Let’s see the forces acting on the stone in two cases, that is, just before the release and just after the release.
As the stone on the elevator there are two forces acting on it at the same time:
The force from the elevator to the stone and the gravitational force.
As the stone is released:
When the stone is released, it loses the contact with the elevator and the force from the elevator becomes zero. Thus, the only force acting on the stone will be gravitational force.
That is, the acceleration of the stone when it is released will be the acceleration due to gravity and is acting downwards.
The acceleration of the stone when it is released= $g$ downwards
When we consider the speed of the stone, as we know, the stone is travelling upwards with the speed of $u$. It will have the same speed and direction just after the release also.
The speed of the stone when it is released= $u$ upwards
So the final answer is option (D), $g$ downwards, $u$ upwards.

Note: The elevator's free-body diagram has three forces, the force of gravity, a downward normal force from the body, and an upward force from the tension in the cable holding the elevator. The combined system of the body and elevator has two forces, a combined force of gravity and the tension in the cable.