A particle is moving with a constant speed v in a circle. magnitude of average velocity after half r

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3-2.Motion in Plane

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

A$2\,v$

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

C$\frac{v}{2}$

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

Solution

Let $R$ be the radius of a circle. Displacement $=\mathrm{AB}=2 \mathrm{R}$
Time taken to go from $A$ to $B,$ $\mathrm{t}=\frac{\pi \mathrm{R}}{\mathrm{v}}$
Average velocity, $\mathrm{v}_{\mathrm{xv}}=\frac{\text { Displacement }}{\text { Time taken }}$
$=\frac{2 \mathrm{R}}{(\pi \mathrm{R} / \mathrm{v})}=\frac{2}{\pi} \mathrm{v}$

Standard 11

Physics

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