Question

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

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

Answer 1

Answer: (C)

Let $R$ be the radius of the circle Displacement of particle $ = r$

Average velocity $=\frac{\text { displacement }}{\text { time }}$
Time $=\frac{\pi R }{2 V }( V =$ velocity $)$
$r =\sqrt{ R ^{2}+ R ^{2}}=\sqrt{2} R$
Average velocity $=\frac{\sqrt{2} R }{\frac{\pi R }{2 V }}=\frac{2 \sqrt{2} V }{\pi}$