Question

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

Answer 1

Hint The center of mass is the concept of position. While considering a system it will be the average position. This average will be according to the masses included in the system. The center of mass can be shifted according to the external factors.

Complete step-by-step answer:
Given that the two persons of masses $55\;{\text{kg}}$ and $65\;{\text{kg}}$ respectively are at the opposite ends of the boat. Then there would be the center of mass which is the average of the positions of the two masses and the whole system. The $55\;{\text{kg}}$ man walks to the $65\;{\text{kg}}$ man and sits with him. The mass of the whole system doesn’t change. And the boat remains in the same state.
The center of mass of a system will remain in the same state unless an external force acts upon that system. The center of mass can be related to Newton’s first law. Hence the boat is in still water no external force is applied to shift the center of mass of the system. So the center of mass shifts by zero only.

Thus the answer is Option C.

Note We have to note that the boat is in still water. If the boat is placed in the water current or somewhere between tides there will be an external force applied to the boat causing the center of mass to shift.