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. `10ms^(-1)`
B. `5sqrt(2)ms^(-1)`
C. `10sqrt(3)`
D. None of these

Answer

C

Explanation

`(T_(max))/(T_(mim.))=((Mv_(l)^(2)+mg)/(L)+mg)/(mv_(H)^(2)/(L)-mg)=4`
or `(v_(L)^(2))/(L)+g=(4v_(H)^(2))(L)-4g`
or `(v_(L)^(2)+2g(2L))/(L)=(v_(H)^(2))/(L)-5g`
or `(v_(H)^(2))/(L)+9g=(4v_(L)^(2))/(L)`
or `(3v_(H)^(2))/(L)=9g` or `v_(H)=sqrt(3gl)`
`=sqrt(3xx10xx10)=10sqrt(3)m//s`