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Question

# A stone of mass 1 kg tied to a light in extensible string of length L=103m is whirling in a circular path of radius L in a vertical plane. 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 10ms2. The speed of stone at the highest point of the circle is

A
20ms
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B
103ms
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C
52ms
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D
10ms
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Solution

## The correct option is D 10msSince 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=mv2BL+mg and TT=mv2TL−mg ∴TBTT=mv2BL+mgmv2TL−mg=41 Or V2B+gLV2L−gL=41 Or V2B+gL=4v2T−4gL but from energy conservation V2B=V2T+4gL ∴V2T+4gL+gL=4V2T−4gL ⇒3V2T=9gL ∴V2T=3×g×L=3×10×103 Or VT=10ms

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