Question

A boy sitting on the top most berth in the compartment of a train which is just going to stop on the railway station, drops an apple aiming at the open hand of his brother situated vertically below his hands at a distance of about $2m$. The apple will fall

• A. In the hand of his brother
• B. Slightly away from the hand of his brother in the direction of the motion of the train.
• C. Slightly away from the hands of his brother in the direction opposite to the direction of the motion of the train.
• D. None of these

Answer 1

The correct option is B Slightly away from the hand of his brother in the direction of the motion of the train.

Given, that the train is going to stop at a railway station, which means that the train is under retardation or is accelerating opposite to the direction of motion.

The boy sitting on the topmost berth drops an apple aiming at the open hand of his brother. Let at this instant, the velocity of the train be $v$. Since, the boy, his brother and the apple are in the same frame, they are also moving with velocity $v$. Hence, when the apple is released, its velocity will be $v$ in the direction of motion of train.

Now, the apple falls downward only under the influence of gravitational force. Since, there are no forces acting in the horizontal direction, it will move with constant velocity $v$ in the horizontal direction. Let it takes time $t$ to come down a height of $2m$. The horizontal distance it covered is given by , $d=vt$

Since, the train is under retardation, which means that the velocity of the train is decreasing. Hence, horizontal distance, the boy's hands will cover in time $t$ will be less than $vt$

Hence, the apple will fall slightly away from the hand of his brother in the direction of motion of the train.