Question

Two persons of masses $55kg$ and $65kg$ respectively are at the opposite ends of a boat. The length of the boat is $3.0m$ and weighs $100kg$ . The $55kg$ man walks up to the $65kg$ man and sits with him. If the boat is in still water the center of mass of the system shifts by
A. $3.0m$
B. $2.3m$
C. Zero
D. $0.75m$

Answer 1

Consider the boat as a system, there is no external force acting on the system. When there is no external force acting, the center of mass of the system is initially at rest and will be at rest.
When considering a system, it will be the average position as center of mass is the concept of position.
The center of mass shifts according to the external force applied.

Complete step by step answer:
Initially, two persons are sitting at the corners of the boat. The length of the boat is $3.0m$ . Given the masses of two persons are $55kg$ and $65kg$ respectively and they are sitting at the opposite ends of the boat. The centre of mass which is average of the positions of the two masses and the whole system. The $55kg$ man walks and sits beside the $65kg$ man. The mass of the complete system does not change and the boat remains at rest.
The centre of mass of the system will remain in the same state unless an unbalanced external force acts upon the system. The centre of mass can also be related to Newton’s first law of motion. Hence, no external force is applied to the boat in still water to shift its centre of mass. So, the centre of mass will shift by zero.

So, the correct answer is “Option C”.

Note:
Please note that the boat was in still water. If the boat was placed in some water with moving current then the water will apply some force on the boat and due to this the centre of mass of the system will change.
Only unbalanced force is responsible to bring about motion or change in an existing system.