Question

A smooth wedge A is fitted in a chamber hanging from a fixed ceiling near the earth’s surface. A block B placed at the top of the wedge takes time T to slide down the length of the wedge and the cable supporting the chamber is broken at the same instant, the block will
(A) Take a time longer than T to slide down the wedge
(B) Take a time shorter than T to slide down the wedge
(C) Remain at the top of the wedge
(D) Jump off the wedge

Answer 1

Hint: In the given question, we have been given a smooth wedge that is fixed into a chamber hanging from a ceiling. We have been told that a block is placed on the top of the wedge. We have been asked what will happen to the block placed on the wedge when the string supporting the chamber is cut. When there is no cable supporting the chamber, it will suffer free fall and a pseudo force will act on it. Let’s see the detailed solution given below.

Complete step by step solution:
A diagrammatic representation of the arrangement of the block and the wedge in the chamber just after the instant when the cable is cut is shown below. The ceiling is labelled in the diagram and the dotted line represents the cable that has been cut.

The weight of the block is acting vertically downwards. Since the entire arrangement will suffer free-fall after the snapping of the call, a pseudo force will act on the block in the upward direction. The pseudo force is equal to the product of the mass of the body and the acceleration it is undergoing. The acceleration in a free fall is the same as acceleration due to gravity. As can be seen in the figure, the magnitude of the pseudo force is equal to the magnitude of the weight of the block and both forces act in the mutually opposite direction. Hence the net force acting on the block would be zero and there would be no normal force acting on the block.
In the absence of any net external force acting on the block, the block would remain in its initial position at the top of the wedge.

Therefore, option (C) is the correct answer.

Note:
In the given question, we were told that the block takes time T to come down to the bottom of the wedge. We don’t need that data as we used a logical approach to arrive at the solution. A pseudo force is a virtual force, also known as inertial force. It is applied when we are observing a system from a non-inertial frame. Any frame of reference that moves with any acceleration is considered a non-inertial frame, as in the case of the given question, the chamber supporting the wedge is a non-inertial frame.