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A stone of mass 1 kg tied to a light inextensible string of length L = 103m, whirling in a circular path in a vertical plane. The ratio of maximum tension to the minimum tension in the string is 4. 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 ms-1

d

20 ms-1

answer is A.

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Detailed Solution

Minimum tension is at topmost point (speed = v) andmaximum tension at bottommost point (speed = u).∵ TmaxTmin=mg+mu2L-mg+mv2L=4⇒ u2=4v2-5gL …(i)and u2=v2+2g(2L) …(ii)On solving Eqs. (i) and (ii), we getv=10 ms-1

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A stone of mass 1 kg tied to a light inextensible string of length L = 103m, whirling in a circular path in a vertical plane. The ratio of maximum tension to the minimum tension in the string is 4. If g is taken to be 10 ms-2 , the speed of the stone at the highest point of the circle is