Question

A man of mass m is suspended in air holding the rope of a balloon of mass M. A climb up the rope, the balloon
1) Moves upward
2) Moves downward
3) Remains stationary

Answer 1

Hint: To solve the following question create a rough diagram for a better understanding of the question. Consider the balloon and the man climbing it be a system, then find the forces acting on the system.

Complete answer:
After assuming that the man and the balloon on which he is climbing is a system, we can find that no external force is acting on the system which means that the centre of mass will remain undisturbed. Initially, when the system which is both the man and the balloon are at rest then the centre of mass of the system will also be at rest. Let us say that the centre of mass of the system will be at the centre as shown in the figure.

According to the question, the man climbs upward therefore, the balloon has to move downward in order to balance the centre of mass of the system.

Hence, option (2) moves downward.

Note:
The centre of mass of a system or a body is defined as a point at which all the masses of a system or whole of the mass of the body of a particle appear to be concentrated. The system of particles means a well-defined collection of a large number of particles which may or may not interact with each other. A system is defined as the collection of two or more objects. An isolated system is defined as the system which is free from the influence of any external force that alters the momentum of the system.