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Question

# The bob of pendulum at rest is given a sharp hit to impart a horizontal velocity of u=√3gl, where l is the length of the pendulum. Select the correct statement.

A
Bob will complete the circle.
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B
String will become slack at top most point.
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C
String will become slack after rotating an angle cos113.
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D
String will become slack after rotating an angle πcos1(13)
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Solution

## The correct option is D String will become slack after rotating an angle π−cos−1(13) Let string slack at B. Applying conservation of energy at point A and B. ΔU+ΔK=0 mg(l+lcosθ)+[12mv2−12mu2]=0 −mg[l+lcosθ]=12mv2−12mu2 v2=u2−2g[l+lcosθ]....(1) When string slack, tension in the string becomes zero. The component of weight in radial direction balance the centrifugal force at this position. mv2l=mgcosθ v2=glcosθ......(2) From equation (1) and (2), 3gl−2gl[1+cosθ]=glcosθ 3cosθ=1⇒θ=cos−1(13) Hence angle rotated α is α=π−θ=π−cos−1(13)

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