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Question

# A simple pendulum is released from rest with the string in horizontal position. The vertical component of the velocity of the bob becomes maximum, when the string makes an angle θ with the vertical. The angle θ is equal to

A
π4
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B
cos1(13)
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C
sin1(13)
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D
π3
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Solution

## The correct option is B cos−1(1√3)At angle theta , l = length of rod v = pendulum velocity u = vertical velocity By energy conservation,mglcosθ=mv22=mu22sin2θDifferentiating wrt θ , and putting dudθ=0; we get, θ=cos−1(1√3)

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