Question

A simple pendulum hangs from the roof of a moving train. The string is inclined towards the rear of the train. What is the nature of motion of the train?
(A) Accelerated
(B) Uniform
(C) Retarded
(D) None of these

Answer 1

Hint: To solve this question, we need to apply the concept of pseudo force. The pseudo force always acts on a body kept inside a non inertial frame and is opposite to the acceleration of the frame.

Complete step-by-step solution
The string of a simple pendulum is vertical in the neutral condition when no external force apart from the vertically downwards force of gravity acts on the bob of the pendulum. According to the question, the string of the given simple pendulum is inclined. This means that a horizontal force must be acting on the bob of the simple pendulum. But there is no real source of horizontal force on the bob mentioned in the given question. So the horizontal force which acts on the bob must be a pseudo force.
We know that the pseudo force acts on a body kept inside an accelerating frame and is equal to the mass of the body times the acceleration of the frame. In this situation, the body is the bob of the pendulum, and the frame is the train.
This means that the train must be in non uniform motion, or must be accelerated or retarded.
Now, we also know that the direction of the pseudo force is opposite to the acceleration of the frame. According to the question, the string is inclined towards the rear of the train. This implies that the direction of the pseudo force is towards the rear of the train. So we get the direction of the acceleration of the moving train towards the front. This means that the nature of motion of the train is accelerated.
Hence, the correct answer is option A.

Note
The above question could also be answered without taking the help of the concept of the pseudo force. We could answer the question using the law of inertia. Since no horizontal force acts on the bob of the pendulum, it will tend to maintain its state of rest and in doing so it will get deflected opposite to the acceleration of the moving train.