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A stone of mass 1 kg tied to a light in...

A stone of mass 1 kg tied to a light inextensible string of lenth `L=(10)/(3)m`, whirling in a circular path in a vertical plane. The ratio of maximum tension to the minimum tension in the string is 4. If g is taken to be `10ms^(-2)`, the speed of the stone at the highest point of the circle is

A

20 m/sec

B

`10sqrt(3)` m/sec

C

`5sqrt(2)` m/sec

D

10 m/sec

Text Solution

Verified by Experts

The correct Answer is:
D
`v_(B) to` velocity at bottom
`v_(T) to` velocity at top
`T_("max")/T_("min") = (((mv_(B)^(2))/L) + mg)/((mv_(T)^(2))/L - mg) = 4/1`
`rArr (v_(B)^(2) + gL)/(v_(T)^(2) - gL) = 4 [therefore v_(B)^(2) = v_(T)^(2) + 4gL]`
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