Q. A particle of mass $m$ is tied to one end of a string of length $l$ and rotated through the other end along a horizontal circular path with speed$\ v$. The work done in half horizontal circle is
A) Zero
B) $\left( \frac{{mv}^{2}}{l} \right)2\pi l$
C) $\left( \frac{{mv}^{2}}{l} \right)\pi l$
D) $\left( \frac{{mv}^{2}}{l} \right)l$
Explanation
(a) Here, centripetal force,
$F = \frac{{mv}^{2}}{l}$
But the angle between force and displacement is $90{^\circ}$ because the direction of centripetal force is always towards the center and direction of displacement is always tangential.
Then work done
$W = \mathbf{F \bullet s} = Fs\cos{90{^\circ}}$
$\Longrightarrow \ \ W = 0$
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Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.