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Question

# A stone of mass 1 kg tied to a light inextensible string of length is whirling in a circular path of radius L in a vertical plane. If the ratio of the maximum tension in the string to the minimum tension in the string is 4 and if g is taken to be 10 m/s2 , the speed of the stone at the highest point of the circle is

A
20 m/sec
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B
103 m/sec
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C
52 m/sec
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D
10 m/sec
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Solution

## The correct option is D 10 m/secSince the maximum tension TB in the string moving in the vertical circle is at the bottom and minimum tension TT is at the top. TB = mvB2L = mg and TT = mvT2L - mg ∴ TBTT = mvB2L+mgmvT2L−mg or vB2+gLvT2+gL = 41 or vB2 + gL = 4vT2 - 4gL but vB2 = vT2 + 4gL ∴ vT2 + 4gL +gL ⇒ 3 vT2 = 3gL ∴ vT2 = 3 × g × L = 3 × 10 × 103 or vT = 10 m/sec

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