Question

A body of mass $m$ stands on end of a wooden plank of length $L$ and mass $M$. The plank is floating on water. If the body 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. $\left(\frac{ml}{M+m}\right)$
• D. $\left(\frac{ML}{M-m}\right)$

Answer 1

The correct option is C $\left(\frac{ml}{M+m}\right)$

Refer to the given figure.

let $x$ be distance of COM from center of plank, $x=\frac{m\ast l/2+M\ast 0}{m+M}=\frac{ml}{2(m+M)}$

Since there are no external forces on plank-body system , COM of system will not change.

As seen from the figure center of plank shifted from ${}^{\prime }{x}^{\prime }$ distance on one side to same distance on other side.

Total displacement will be "2x " $=2\times \frac{ml}{2(m+M)}=\frac{ml}{(m+M)}$