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 theta with the vertical. Workdone by the force is

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 )

Author: Rajesh Jha

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