A body of mass m is suspended by a rod of length L that pivots without friction (see figure). The mass is slowly lifted along a circular arc to a height h. 

a. Assuming that the only force acting on the mass is the gravitational force, show that the component of this force acting along the arc of motion is F = mg sin θ.

b. Noting that an element of length along the path of the pendulum is ds = L dθ, evaluate an integral in θ to show that the work done in lifting the mass to a height h is mgh.

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