Question

A particle is moving with constant speed in a circular path. Find the ratio of average velocity to its instantaneous velocity when the particle describes an angle $\theta =\frac{\pi }{2}$.

• A. $\frac{2\sqrt{2}}{\pi }$
• B. $\frac{2}{\pi }$
• C. $\frac{2\sqrt{2}}{\sqrt{\pi }}$
• D. $\frac{\sqrt{2}}{\pi }$

Answer 1

The correct option is A $\frac{2\sqrt{2}}{\pi }$

Time taken to describe angle $\theta ,t=\frac{\theta }{\omega }=\frac{\theta R}{v}=\frac{\pi R}{2v}$

Displacement $=\sqrt{R^2+R^2}=\sqrt{2}R$
Average velocity = $\frac{Totaldisplacement}{Totaltime}=\frac{\sqrt{2}R}{\pi R/2v}=\frac{2\sqrt{2}}{\pi }v$
Instantaneous velocity $=v$
The ratio of average velocity to its instantaneous velocity = $\frac{2\sqrt{2}}{\pi }$.