a rigid body of mass m is moving in a circle of radius r with a constant speed v. the force on the body is mv^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

Dear student,

Since at every point on the circumference, the direction of this force is radially inwards, but the instantaneous displacement of the particel is along the tangent(hence they being at right angles to each other), the work done by this force at all points is zero. Hence the total work done in moving over the circumference for any length is zero.

Regards.