Question

A particle is moving with constant speed $v$ in circle. What is the magnitude of average velocity after half rotation?

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

Answer 1

Answer: (B)

$2\frac{v}{\pi }$

The particle starts from point $P$ and after half rotation, it reaches at $Q$ via path $PMQ$.

Distance covered by particle to reach at $Q$ is $d=\pi R$

Time taken, $t=\frac{d}{v}=\frac{\pi R}{v}$

Displacement of the particle, $s=PQ=2R$

$\therefore$ Average velocity, $v_{avg}=\frac{s}{t}=\frac{2R}{\frac{\pi R}{v}}=\frac{2}{\pi }v$