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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/sIn 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, TA−Mg=MV2AL ⇒TA=Mg+MV2AL=Tmax For circular motion at the highest point C, Tc+Mg=MV2CL ⇒Tc=MV2CL−Mg=Tmin Given that ⇒TmaxTmin=41=MV2AL+MgMV2CL−Mg⇒V2A+gLV2C−gL=41 But from work energy theorem, V2A=V2C+2g(2L)=V2C+4gL ⇒V2C+5gLV2C−gL=41⇒3V2C=9gL ⇒V2C=3gL=3×10×103=100 ∴VC=10 m/s Hence, the correct answer is option (d).

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