A stone of mass 2 kg tied to a light inextensible string of length `(5)/(3)` m is whirling in a circular path in a vertical plane. If the ration of the maximum tension to the minimum tension in the string is 4 then the speed of the stone at the highest point of the circle is (g= `10 ms^(-2))`

Options

A. `20 ms^(-1)`
B. `10sqrt(3) ms^(-1)`
C. `sqrt(50) ms^(-1)`
D. `10 ms^(-1)`

Answer

C

Explanation

Tension is maximum at bottom of vertical circle and it is
`T_(1)= (mv^(2))/(r )+mg`

Tension is minimum at top and it is
`T_(2) = ("mu"^(2))/(r ) 5mg`
Given ratio `(T_(1))/(T_(2)) = 4 implies 21 mg = 3 ("mu"^(2))/( r) `
`implies mu^(2)= 7rg `
Now velocity at top
`nu=sqrt(mu^(2)-4rg)=sqrt(7rg-4rg)=sqrt(3rg)=sqrt(50)`m/s