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Question

A small stone of mass 200 g is tied to one end of a string of length 80 cm. Holding the other end in the hand, the stone is whirled in a vertical circle. What is the minimum speed that needs to be imparted at the lowest point such that the stone is just able to complete the vertical circle?(Take g=10 m/s2)

A
4 m/s
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B
5.13 m/s
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C
6.32 m/s
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D
7 m/s
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Solution

The correct option is C 6.32 m/s

At the top most point,
T+mg=mv2AR
If stone is just able to complete vertical ciruclar motion, then at the top most point, T=0
mg=mv2AR
vA=Rg

Applying law of conservation of energy at A & B (Taking reference point at A)
UA+KEA=UB+KEB
mg (2R)+12mV2A=0+12mV2B
VB=5gR
=5×10×0.8
=6.32 m/s

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