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 centre of mass of the 'man plus boat' system will remain stationary with respect to water :

• A. only when the man is stationary initially and finally
• B. only if the man moves without acceleration on the boat
• C. only if the man and the boat have equal masses
• D. in all cases

Answer 1

The correct option is D in all cases

Motion of centre of mass is affected by net external force only.

$\overrightarrow{F_{external}}=M\overrightarrow{a_{CM}}$

As there is no external force, $⟹\overrightarrow{a_{CM}=0}$ Or $u_{CM}=v_{CM}$

Also the man as well as the boat are stationary initially i.e $u_{CM}=0$

$⟹$ $v_{CM}=0$ i.e their centre of mass will also remain stationary finally in all cases.