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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