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Question

A stone of mass 1 kg tied to a light string of length 103 m is whirled in a vertical circle. If the ratio of the maximum tension to minimum tension is 4 and g=10 m/s2, then the speed of the stone at the highest point of the circle is

A
0 m/s
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B
20 m/s
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C
10 m/s
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D
5 m/s
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Solution

The correct option is C 10 m/s

Let vo & vt be the velocities at the bottom and top of the circle.
Tension will be maximum at the bottom of the circle.
Tmax=mv2or+mg ------(1)
Tension will be minimum at the top of the circle.
Tmin=mv2trmg -------(2)

TmaxTmin=4 (given)
mv2or+mgmv2trmg=4 -----(3)

Applying conservation of energy at points A & B, taking A as a reference point
KEA+PEA=PEB+KEB
12mv2o+0=mg(2r)+12mv2t
v2ov2t2=2gr -------(4)

From equation (3)
mv2or+mg=4mv2tr4mg
5mg=4mv2trmv2or
4v2tv2o=5gr ---------(5)
From equation (4)
v2ov2t=4gr(6)

By solving Equation (5) & (6)
3v2t=9gr
v2t=3gr
vt=3gr
vt=3×10×103=10 m/s

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