A dense sphere of mass M is placed at the centre of a circle of radius R. Find the work done, when a particle of mass m is brought from A to B along a circle as shown in the figure.
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E=PE+KE From energy conservation, 21mvA2+(PE)A=21mvB2+(PE)B Since speed does not change from A to B, KE remains same. Distance of the particle at A and B is equal to the radius of the the circle. PE=−RGMm Hence, (PE)A=(PE)B Hence, work done is zero as there is no change in total energy E from A to B.