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 weights 100kg. The 55kg man walks up to the 65kg man and sits with him. If the boat is in still water the centre of mass of the system shifts by:
(A) Zero
(B) \[\;0.75m\]
(C) \[\;3.0m\]
(D) \[2.3m\]

Answer 1

Hint The concept of centre of mass of a system enables us, in describing the overall motion of the system by replacing the system by an equivalent single point, where the entire mass of the body or system is supposed to be concentrated.

Complete step by step answer:
Centre of mass of a system of particles or in a body can be defined as a point at which the total mass of the system is supposed to be concentrated. Centre of mass of the system represents the entire body. On application of external forces, the centre of mass of the system of particles moves in the same way as a point having mass equal to that of the whole system.
Now when external force is zero then the system will remain at rest so the centre of mass does not move.
Let us match this with the options given
Zero :- as external forces in the given question is zero then centre of mass will show no displacement. So this option is correct.
\[\;0.75m\]:- on application of external force centre of mass moves, but in this case external forces are zero thus this option is not correct.
\[\;3.0m\]:- as external forces are zero centre of mass remains at rest. Thus this option is also not correct.
\[2.3m\]:- when external forces are zero centre of mass have zero displacement. So this option is not correct.

Our required answer is a that is zero

Note
If a system consists of more than one particle and net external force on the system in a particular direction is zero with the centre of mass at rest. Motion of the centre of mass of a system or object is not affected by any of internal forces.