Question

A boy sitting on the topmost berth in the compartment of a train, which is just going to stop on a railway station, drops an apple aiming at the open hand of his brother sitting vertically below his hand. The apple will fall

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

Answer 1

The above question is directly related to Newton's law of motion, there are three laws of motion namely first law of motion, second law of motion and third law of motion. These laws are applied to objects which are idealised as single point masses i.e. the size and shape of the objects body is neglected to focus more on its motion.

Complete step by step answer:
From the above data, it is evident that the boy was in a motion train which was about to stop after a while. Before discussing the question let's recall the concepts of Newton's laws of motions:

-Newton's first law:
The first law states that an object will remain at rest unless and until an external force acts on it. Similarly an object in motion will stay in motion unless an external force disturbs it. First law can be expressed mathematically when the mass is non-zero constant as:
$\sum F = 0 \Leftrightarrow \dfrac{{dv}}{{dt}}$

-Newton's second law:
From the second law of motion, we know that a body’s rate of change of momentum is directly proportional to the applied force. The direction of the change in momentum will be the same as the direction of the applied force.
It is mathematically expressed as:
$F = \dfrac{{dv}}{{dt}} = \dfrac{{d(mv)}}{{dt}}$
Where momentum, $P = mv$ (product of mass and velocity)

-Newton's third law of motion:
From Newton's third law of motion we know that, for every action takes place, there is always an equal and opposite reaction. This law is sometimes known as action - reaction law.

Now coming to the question, the boy was aiming the apple towards the vertically downward direction of his brother's hand. When the apple leaves the hand of the boy, the apple is in the state of free fall whereas the boy will feel the retardation motion when the train pulls to a stop due to the third law of motion.
As the apple doesn't follow any retardation, so when it falls down it will fall slightly away from the hand of his brother in the direction of the motion of the train.

Hence option (B) is the correct answer.

Note: The above question heavily emphasizes Newton's law of motion, so one should have a proper concept of the motion laws to understand and reply to the answer. The free fall mentioned in the solution refers to the state when a body falls it accelerates equal to the acceleration due to gravity.