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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 10ms
Since 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=mv2TLmg
TBTT=mv2BL+mgmv2TLmg=41
Or V2B+gLV2LgL=41
Or V2B+gL=4v2T4gL
but from energy conservation V2B=V2T+4gL
V2T+4gL+gL=4V2T4gL
3V2T=9gL
V2T=3×g×L=3×10×103
Or VT=10ms

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