Question

Journey in a train is adventurous particularly when you have a seat. The girl sitting near the window ate a banana and dropped the peel from the window. Her co-passenger looking through the window found that it dropped vertically down and touched the ground in 0.2s. After sometime she requested her sister sitting on the upper berth to drop a chocolate bar. The sister dropped the bar, but it fell in front of the girl instead of reaching her hand. She was angry but the co-passenger calmed her by saying that she dropped exactly in line of your hand but as the train was accelerating it did not reach you and fell in front of you. If the train would have moved with uniform velocity the chocolate will fall

(A) behind her hands
(B) towards left
(C) towards right
(D) in her hands

Answer 1

Hint: To reach the answer to the question, we should use the properties of Newton’s laws of motion. Finding the differences between the movement of an object while moving with uniform velocity and while moving with an acceleration will help us.

Complete step by step answer:Let us have a look at Newton’s laws of motion. According to Newton’s first law of motion, every object will continue in its state of rest or continue to move with uniform velocity until and unless urged by an external unbalanced force. Inertia is the property by which a body tries to combat the changes brought to its state of rest or of uniform motion by an external factor. Hence, from the first law, we see that a force is necessary to change the state of rest or uniform motion of a body.

Since the force changes the state of rest or uniform motion of a body, we can say that the force produces acceleration according to Newton’s second law of motion.

From the above explanation, we can say that a force produces acceleration by changing the state of rest or uniform motion of a body. It is said that the chocolate dropped by the sister on the upper berth fell in front of the girl. Here the horizontal component of the velocity with which the girl dropped the chocolate is the same as the velocity of the train at the time of dropping. The falling of the chocolate in front of the girl implies the deceleration of the train. Due to the deceleration of the train, the girl in the lower berth moved only a small distance. Since the horizontal velocity had a high value before deceleration occurred, the chocolate moved a longer distance than the girl resulting in the falling of the chocolate in front of the girl.

Now, let us look into the case where the train is moving with a uniform velocity. When the train is moving with uniform velocity, the acceleration of the chocolate will be zero. As we said, due to the property of inertia, the chocolate remains in the same state of motion since there is no force causing the acceleration. The horizontal velocity of the chocolate is the same as the train’s velocity, which is uniform. Hence, we can say that the distance moved by the girl and the chocolate in the horizontal direction will be the same.

The gravitational force will cause only the vertical movement of the chocolate. Hence, we can conclude that the chocolate will fall down vertically into the hands of the girl when the train is moving with uniform velocity.
Therefore, the option (D) is correct.

Note:We should also note that if the train accelerates, the chocolate would have fallen behind the girl. It is because if the train accelerates, the girl moves a longer distance while the chocolate moves a smaller distance.