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

Options

A. 20 m/sec
B. `10sqrt(3)` m/sec
C. `5sqrt(2)` m/sec
D. 10 m/sec

Answer

D

Explanation

`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]`