Question

A lift is moving with acceleration a. A man in the lift drops a ball inside the lift. The acceleration of the ball as observed by a man in the lift and a man standing stationary on the ground are, respectively.
A. g, g
B. g-a, g-a
C. g-a, g
D. a, g

Answer 1

We will take the ground to be our frame of reference and define the sign convention for motion. Then we will find the acceleration of the ball with reference to the ground and the relative acceleration of the ball with reference to the lift.
Formula used:
F = ma

Complete answer:
First let us define the ground as our frame of reference as it stays still during the problem and is an inertial frame as there is no acceleration on it. The lift has an acceleration of a. Let us define the acceleration downward as positive and upward as negative. With this sign convention the direction of acceleration due to gravity will be positive. Now let us define the acceleration of the ball with reference to ground as ${{a}_{bg}}$. This will be equal to g, the acceleration due to gravity as gravity is the only force acting on the ball and the ground is an inertial frame, this will be the acceleration of the ball observed by the person on ground. Following figure shows the acceleration of both the lift and the ball as seen by the person on ground

As ‘a’ is the acceleration of lift. Then the relative acceleration of the ball with reference to lift can be found by subtracting the acceleration of lift with reference to ground from the acceleration of the ball with reference to ground which will come out to be ${{a}_{bg}}-a$. And as ${{a}_{bg}}$ is equal to g, the acceleration of the ball as seen by the observer in lift will be g-a.

So, the correct answer is “Option C”.

Note:
We can also solve this question using the concept of pseudo forces. The lift can be considered as an inertial frame if we consider a pseudo force on objects in that frame which is caused due to the acceleration of the lift. The pseudo force will cause an acceleration same in magnitude but in the opposite direction to the acceleration of the lift. And we will get the same answer as of now.