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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=mv2tr−mg -------(2) TmaxTmin=4 (given) ⇒mv2or+mgmv2tr−mg=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 v2o−v2t2=2gr -------(4) From equation (3) mv2or+mg=4mv2tr−4mg ⇒5mg=4mv2tr−mv2or 4v2t−v2o=5gr ---------(5) From equation (4) v2o−v2t=4gr−−−−−−−−(6) By solving Equation (5) & (6) 3v2t=9gr v2t=3gr vt=√3gr vt=√3×10×103=10 m/s

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