Question

A man stands at one end of the open truck which can run on frictionless horizontal rails. Initially, the man and the truck are at rest. Man now walks to the other end and stops. Then which of the following is true?
A. The truck moves opposite to the direction of motion of the man even after the man ceases to walk.
B. The centre of mass of the man and the truck remains at the same point throughout the man’s walk.
C. The kinetic energy of the man and the truck are exactly equal throughout the man’s walk.
D. The truck does not move at all during the man’s walk.

Answer 1

Hint: Considering the man-truck as a system, with no external force, we can solve the question. Clearly the system will have a centre of mass, and follows conservation of momentum. But it will not have any kinetic energy.

Complete step by step solution:
Let us assume that the man and the truck to be a system. Since there is no friction on the rails, we can say that there is no external force acting on the system. This means that the centre of mass of the system does not change. Also, the momentum of the system is conserved, thus when the man moves towards the end of the truck, the truck will move in the opposite direction. If the man stops, then the truck will also stop.
Centre of mass is the point in the body where the whole mass of the body is supposed t be concentrated. For symmetrical, rigid objects, the centre of mass is at the geometrical centre of the object.
Hence, the answer is B. The centre of mass of the man and the truck remains at the same point throughout the man’s walk.

Note: Instead of considering the man and the truck as two different systems, consider them as one system, which has no external force. Also, due to conservation of momentum, the truck moves only when the man moves, however the direction of the truck and man will be opposite.