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

Answer

D

Explanation

`v^(2)=u^(2)-2gxx2Limpliesu^(2)=v^(2)+4gL`
`T_(1)-mg=(m u^(2))/(L)impliesT_(1)=mg+(m u^(2))/(L)=T_(max)`
`T_(2)+mg=(mv^(2))/(L)impliesT_(2)=(mv^(2))/(L)-mg=T_(min)`
`(T_(max))/(T_(min)=(mg+(mu^(2))/(L))/((mv^(2)/(L)-mg)=4`
`gL+u^(2)=4(v^(2)-gL)=4v^(2)-4gL`
`gL+v^(2)+4gL=4v^(2)-4gL`
`v=sqrt(3gL)=sqrt(3xx10xx(10)/(3))=10m//s`