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 $\theta=\frac{\pi}{2}$

Answer 1

$\quad$ Time taken to describe angle $\theta, t=\frac{\theta}{\omega}=\frac{\theta R}{v}=\frac{\pi R}{2 v}$ Average velocity$=\frac{\text { Total displacement }}{\text { Total time }}=\frac{\sqrt{2} R}{\pi R / 2 v}=\frac{2 \sqrt{2}}{\pi} v$ Instantaneous velocity $=v$

The ratio of average velocity to its instantaneous velocity $=\frac{2 \sqrt{2}}{\pi}$ Ans.