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Question

A stone of mass 1kg tied to a light inextensible string of length L=103m 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 is 4 and if g is taken to be 10 m/s2, then speed of stone at the highest point of the circle is

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

The correct option is D 10m/sec
Let 'v' be the velocity at the top point
Velocity at the bottom point is =v2+2gd =v2+4gr
Maximum tension in string appears when the stone is at the bottom of the circle.
Tmax=m(v2+4gr)r+mg
Minimum tension appears in a string when the stone is at the top of the circle.
Tmin=mv2rmg
TmaxTmin=v2+4grr+gv2rg =4
On solving the equation we get, v=10 m/s

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