Question

A rod of length $l$ lying horizontally on a smooth horizontal surface is moving with centre of mass velocity $v$ and angular velocity $\omega =\frac{2v}{l}$. The distance covered by one of the end points of the rod during the time the rod completes one full rotation is $nl$. Find the value of $n$

• A. $\pi$
• B. $2\pi$
• C. $4\pi$
• D. $1$

Answer 1

The correct option is A $\pi$

Given,

Distance covered during one rotation is $nl$

Angulate velocity, $\omega =\frac{2u}{l}$

Angular velocity, $\omega =\frac{2\pi }{T}\Rightarrow T\omega =2\pi$

Distance, $S$

$S=vT=\left(\frac{l\omega }{2}\right)T$

$\Rightarrow nl=\frac{l}{2}\times 2\pi$

$\Rightarrow n=\pi$

Hence, value of $n$ is $\pi$ .