First slide

Centre of mass(com)

Question

A man stands at one end of a boat which is stationary in water. Neglect water resistance. The man now moves to the other end of the boat and again becomes stationary. The center of mass of the 'man plus boat' system will remain stationary with respect to water

Moderate

A

only when the man is stationary initially and finally
B

only ifthe man moves without acceleration on the boat
C

only if the man and the boat have equal masses
D

in all cases

Solution

There is no external force acting on the system of 'man + boat'.
$⟹ {\vec{a}}_{CM} = 0 \Rightarrow u_{CM} = v_{CM} Also the man as well as the boat are stationary initially i.e u_{C M} = 0 \Rightarrow v_{C M} = 0 i.e their centre of mass will also remain stationary finally in all cases.$

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