Question

A 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 constant speed. The speed of the insect 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 A $\frac{l}{t}\left[\frac{M}{M+m}\right]$


Co-ordinates of $COM$ will not change as no external force is present.
$\Rightarrow m(l-x)=Mx\Rightarrow x=\frac{ml}{m+M}$
Distance moved by insect w.r.t. ground is $l-x=l-\frac{ml}{m+M}=\frac{M}{m+M}l$
Speed of the insect as seen from the ground : $=\frac{\text{distance}}{\text{time}}=\frac{Ml}{t(M+m)}$