Question

A boy of mass $m$ stands on one end of a wooden planck of length $L$ and mass $M$. The plank is floating on water. If the boy walks from one end of the plank to the other end at a constant speed, the resulting displacement of the plank is given by

• A. $\frac{mL}{M}$
• B. $\frac{ML}{m}$
• C. $\frac{mL}{M+m}$
• D. $\frac{mL}{M-m}$

Answer 1

Answer: (C)

Before the boy starts walking on the plank. both the boy and the plank are at rest. So total momentum of (boy +plank) system is zero. If the boy walks with a speed $v$ on the plank and as a result if the speed of the plank in the opposite direction is $V$
Then the total momentum of system is
$mv-(M+m)V=0$
or $\frac{V}{u}=\frac{m}{(M+m)}$
Since distance moved is proportional to speed, the displacement $L^{\prime }$ of the plank is given by
$\frac{L^{\prime }}{L}=\frac{V}{V}=\frac{m}{(M+m)}$
or $L^{\prime }=\frac{mL}{(M+m)}$