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Q.

A stone of mass 1 kg tied to a light inextensible string of length L = 10/3 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 ms-2, the speed of the stone at the highest point of the circle is

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a

10ms−1

b

53ms−1

c

103ms−1

d

20ms−1

answer is A.

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Detailed Solution

m=1kg⇒L=103mTmaxTmin=4 .........(i)and VL=VH2+4gLTension at highest point, Tmin=mvH2K−mgTension at lowest point,Tmax=mvL2/L+mg=mvH2+4gLL+mgNow Eq. (i) can be written asmvH2+4gLL+g=4×mvH2L−g⇒vH=3gL=10ms−1

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