Question

Strip of wood of mass $M$ and length $l$ is placed on a smooth horizontal surface. An insect of mass $m$ starts at one end of the strip and walks to the other end in time $t$, moving with a constant speed. Then the speed of the strip as seen from the ground is

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

Answer 1

The correct option is B $\frac{l}{t}\left(\frac{m}{M+m}\right)$

Since the strip is not fixed, it is free to move on a horizontal surface.
Also, no external forces are present. So, the position of centre of mass remains fixed Initially, centre of mass of system is given by
$x_i=\frac{m\times 0+\frac{Ml}{2}}{m+M}=\frac{Ml}{2(M+m)}$
When the insect reaches the other end,
$x_f=\frac{ml+M(\frac{l}{2}-x)}{m+M}$
As $x_i=x_f,$ we get
Thus, the strip moves to the left by,
$x=\frac{2ml+Ml-Ml}{2(M+m)}=\frac{2ml}{2(M+m)}=\frac{ml}{M+m}$
The speed of strip as seen from ground is
$v_{sg}=\frac{ml}{(M+m)t}=\frac{l}{t}\left(\frac{m}{(M+m)}\right)$