A body of mass m is performing a UCM in a cir | vedclass

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(A) In uniform circular motion $(UCM)$,the centripetal force acting on the body is always directed towards the center of the circle.The velocity of th

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Zero

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(A) In uniform circular motion $(UCM)$,the centripetal force acting on the body is always directed towards the center of the circle.The velocity of the body is always directed along the tangent to the circular path at any given point.Since the radius (position vector) is perpendicular to the tangent,the centripetal force is always perpendicular to the instantaneous velocity vector of the body.The work done $W$ is given by the dot product of force $\vec{F}$ and displacement $d\vec{s}$,which is $W = \int \vec{F} \cdot d\vec{s}$.Since $\vec{F} \perp d\vec{s}$ at every point in $UCM$,the angle between them is $90^{\circ}$.Therefore,the work done $W = \int F \cdot ds \cdot \cos(90^{\circ}) = 0$.Thus,the work done by the centripetal force in moving the body through any fraction of the circular path,including $\left(\frac{2}{3}\right)$ rd,is always zero.

$A$ body of mass $m$ is performing a $UCM$ in a circle of radius $r$ with speed $v$. The work done by the centripetal force in moving it through $\left(\frac{2}{3}\right)$ rd of the circular path is

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