Question

A man of mass $m$ moves with a constant speed on a plank of mass $M$ and length $l$, kept initially at rest on a frictionless horizontal surface, from one end to the other in time $t$. The speed of the plank relative to ground while man is moving, is :

• A. $\frac{l}{t}\left(\frac{M}{m}\right)$
• B. $\frac{l}{t}\left(\frac{m}{m+M}\right)$
• C. $\frac{l}{t}\left(\frac{M}{M+m}\right)$
• D. $Noneofthese$

Answer 1

Answer: (B)

$\frac{l}{t}\left(\frac{m}{m+M}\right)$

Let the distance moved by the plank be $x.$

So the distance that the man will move is $l-x.$

Applying Conservation of Linear Momentum$,$

$Mx=m(l-x)$

$Mx=ml-mx$

$Mx+mx=ml$

$x(M+m)=ml$

$x=ml/(M+m)$

Distance moved by the plank in $t$ seconds is $ml/(M+m).$

$\begin{array}{c}Speed=\frac{Distance}{Time}=\frac{ml}{\left(M+m\right)t}\end{array}$

$=\frac{l}{t}\left(\frac{m}{m+M}\right)$

Hence, option $\left(B\right)$ is correct answer.