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Question

# A bob of a stationary pendulum is given a sharp hit to impart it a horizontal speed of √3gl. Find the angle rotated by the string before it becomes slack.

A
θ=cos1(23)
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B
θ=cos1(34)
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C
θ=cos1(13)
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D
θ=cos1(53)
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Solution

## The correct option is C θ=cos−1(−13)V=√3gl12mv2−12mu2=−mghv2=u2−2g(1+cosθ)⇒v2=3gl−2gl(1+cosθ)--------------(1)Again,mv2l=mgcosθv2=lgcosθfrom equation (1) and (2), we get3gl−2gl−2glcosθ=glcosθ 3cosθ=1⇒cosθ=13θ=cos−1(13)So, angle rotated before the string becomes slack=1800−cos−1(13)=cos−1(13)Hence,option (C) is correct answer.

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