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

Options

A. `20 m//sec`
B. `10 sqrt3 m//sec`
C. `5 sqrt2 m//sec`
D. `10 m//sec`

Answer

D

Explanation

Since the maximum tension `T_(B)` in the string moving to the vertical circle is at the bottom and minimum tension `T_(T)` is at the top.
`:. T_(B) = (mv_(B)^(2))/(L) + mg and T_(T) = (mv_(T)^(2))/(L) - mg`
`:. (T_(B))/(T_(T)) = ((mv_(B)^(2))/(L) + mg)/((mv_(T)^(2))/(L) - mg) = (4)/(1) or (v_(B)^(2) + gL)/(v_(T)^(2) - gL) = (4)/(1)`
or `v_(B)^(2) + gL = 4v_(T)^(2) - gL but v_(B)^(2) = v_(T)^(2) + 4gL`
`:. v_(T)^(2) + 4gL+ gL = 4v_(T)^(2) - 4gL implies 3v_(T)^(2) = 9gL`
`:. v_(T)^(2) = 3 xx gxx L = 3 xx 10 xx (10)/(3) or v_(T) = 10 m//sec`