A body of mass m moves in a circle of radius | vedclass

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(B) In uniform circular motion,the centripetal force $F = \frac{mV^2}{r}$ is always directed towards the center of the circle.At any given instant,the

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(B) In uniform circular motion,the centripetal force $F = \frac{mV^2}{r}$ is always directed towards the center of the circle.At any given instant,the displacement $ds$ of the body is along the tangent to the circular path.The angle between the centripetal force (directed towards the center) and the displacement (along the tangent) is always $90^\circ$.The work done $W$ is given by the integral $W = \int F \cdot ds = \int F \cos(90^\circ) ds$.Since $\cos(90^\circ) = 0$,the work done by the centripetal force is $0$ for any displacement,including half the circumference.

$A$ body of mass $m$ moves in a circle of radius $r$ with a constant speed $V$. $A$ force of $mV^2/r$ acts towards the center of the circle. Find the work done by this force when the body covers half the circumference of the circle.

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