Problem 150 - A Complete Resource Book in Physics for JEE Main

Question

A lift is moving down with an 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, (A) \(g, g\) (B) \(g-a, g,-a\) (C) \(g-a, g\) (D) \(a, g\)

Step-by-Step Solution

Answer

The short answer is: The acceleration of the ball as observed by the man inside the lift is \(g-a\) and the acceleration of the ball as observed by the man on the ground is \(g + a\). The best choice is (C) \(g-a, g\).

Step 1: Consider the man inside the lift as the observer

From the perspective of the man inside the lift, the ball is acted upon by only the gravitational force with acceleration \(g\). Since the lift is moving downward with acceleration \(a\) and the ball is moving along with it, the man inside the lift will observe the ball as having an acceleration of \(g-a\).

Step 2: Consider the man on the ground as the observer

For the man standing stationary on the ground, the ball is acted upon by two forces: the gravitational force and the downward acceleration of the lift. Therefore, the man on the ground will observe the ball falling with an acceleration of \(g + a\) (since downward motion is considered negative).

Step 3: Identify the correct answer

Based on our analysis, the acceleration of the ball as observed by the man inside the lift is \(g-a\) and the acceleration of the ball as observed by the man on the ground is \(g + a\). Comparing our results with the given options, we can see that none of the options exactly match our findings. However, option (C) is partially correct, as it correctly states the acceleration observed by the man inside the lift. Since none of the other options are more accurate, we can consider option (C) as the best choice. So, the answer is (C) \(g-a, g\).