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A body of mass m is moving in a circle of radius r with a constant speed v. The force on the body is $\frac{m{v}^{2}}{r}$ and is directed towards the centre. What is the work done by this force in moving the body over half the circumference of the circle

(1) $\frac{m{v}^{2}}{\pi {r}^{2}}$

(2) Zero

(3) $\frac{m{v}^{2}}{{r}^{2}}$

(4) $\frac{\pi {r}^{2}}{m{v}^{2}}$