Q: An object of mass m is tied to a string of length L and a variable horizontal force is applied on it which starts at zero and gradually increases until the string makes an angle θ with the vertical. Work done by the force F is:

(a) mgL(1-sinθ )

(b) mgL

(c) mgL(1-cosθ )

(d)mgL(1 + cosθ )

Sol: Work done by the external force = Δ E of the system (object)

= ΔPE (since ΔKE=0 )

= mgh = mg (L – L cosθ )

= mgL (1 – cosθ )