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Question

A stone of mass 1 kg tied to a light inextensible string of length L=103 m 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 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/s
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B
103 m/s
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C
52 m/s
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D
10 m/s
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Solution

The correct option is D 10 m/s
In case of circular motion in a vertical plane, the tension is maximum at the lowest point A but minimum at the highest point C.
For circular motion at lowest point A,
TAMg=MV2AL
TA=Mg+MV2AL=Tmax

For circular motion at the highest point C,
Tc+Mg=MV2CL
Tc=MV2CLMg=Tmin

Given that
TmaxTmin=41=MV2AL+MgMV2CLMgV2A+gLV2CgL=41

But from work energy theorem, V2A=V2C+2g(2L)=V2C+4gL
V2C+5gLV2CgL=413V2C=9gL
V2C=3gL=3×10×103=100
VC=10 m/s
Hence, the correct answer is option (d).

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