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Question

# A stone of mass 1 kg tied to a light inextensible string of length. L=103 metre is whirling in a circular path of radius, L, in a vertical plane. If the ratio of maximum tension 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 circle is :

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

## The correct option is C 10 m/sWhen the stone is revolved in a vertical circle, tension is maximum at bottom and minimum at top. So we have, Tension at bottom as TB and Tension at top as TT.We know, TBTT=4⇒mv2BL+mgmv2TL−mg=4⇒mv2BL+mg=4(mv2TL−mg)⇒mv2BL=4mv2TL−5mg⇒mv2B=4mv2T−5mgL ......(I)Now using the law of conservation of energy, at top and bottom of the vertical circle, we have:12mv2T+2mgL=12mv2B⇒mvB2=mvT2+4mgL ......(II)from (I) and (II), we have 4mv2T−5mgL=mvT2+4mgL⇒3mv2T=9mgL⇒vT=√3gL⇒vT=√3×10×(103)=10 m/s

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