JEE MAIN - Physics (2002 - No. 57)
A lift is moving down with acceleration $$a.$$ A man in the lift drops a ball inside the lift. The acceleration of the ball as observed by the man in the lift and a man standing stationary on the ground are respectively
$$g,g$$
$$g-a, g-a$$
$$g-a, g$$
$$a, g$$
Explanation
Let acceleration of ball = $${\overrightarrow a _b}$$ and acceleration of man is = $${\overrightarrow a _m}$$
With respect to the man standing in the lift, the acceleration of the ball
$${\overrightarrow a _{bm}} = {\overrightarrow a _b} - {\overrightarrow a _m}$$
$$ \Rightarrow {a_{bm}} = g - a$$
Where $$a$$ is the acceleration of the man as the acceleration of the lift is $$a$$.
With respect to the man standing in the lift, the acceleration of the ball
$${\overrightarrow a _{bm}} = {\overrightarrow a _b} - {\overrightarrow a _m}$$
$$ \Rightarrow {a_{bm}} = g - a$$
Where $$a$$ is the acceleration of the man as the acceleration of the lift is $$a$$.
With respect to the man standing on the ground the acceleration of the ball
$${\overrightarrow a _{bm}} = {\overrightarrow a _b} - {\overrightarrow a _m}$$
$$ \Rightarrow {a_{bm}} = g - 0$$
$$ = g$$
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