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Q.

A stone of mass 1 kg tied to a light inextensible string  of length L = 10 m is whirling in a circular path of radius L in vertical plane. If 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 10 ms-2, the speed of the stone at the highest point of the circle is

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a

10 ms-1

b

52 ms-1

c

103

d

None of these

answer is C.

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Detailed Solution

TmaxTmin = Mv12+mgL+mgmvH2L-mg = 4or   vL2L+g = 4vH2L-4gor vH2+2g(2L)L = 4vH2L-4gor vH2+2g(2L)L = 4vH2L-5gor vH2L+9 g = 4vH2Lor 3vH2L = 9g or vH = 3gL = 3×10×10 = 103 m/s
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