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Question

A particle is suspended from a fixed point by a string of length 5 m. It is projected from the equilibrium position with such a velocity that the string becomes slack after the particle has reached a height of 8 m above the lowest point. Find the velocity of the particle, just before the string becomes slack.(take g=10 m/s2)

A
30 m/s
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B
40 m/s
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C
50 m/s
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D
60 m/s
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Solution

The correct option is A 30 m/s
For finding the velocity of the particle just before the slackness we have the condition of tension at point B, TB=0

Here the angle θ=37o, as sinθ=35
Thus, by the FBD of the bob at the point B we get

mv2l=mg cos 53o (T=0)
v=gl cos 53o=30 m/s

Hence option A is the correct answer

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