A body of mass `m` is rotated in a vertical circle with help of light string such that velocity of body at a point is equal to critical velocity at that point. If `T_(1), T_(2)` be the tensions in the string when the body is crossing the highest and the lowest positions then the following relation is correct

Options

A. `T_(2)-T_(1) = 6mg`
B. `T_(2)-T_(1) = 4mg`
C. `T_(2)-T_(1) = 3mg`
D. `T_(2)-T_(1) = 2mg`

Answer

A

Explanation

`T_(1) = (m v_(1)^(2))/(r )-mg, T_(2) = (m v_(2)^(2))/(r )+mg`
`v_(2)^(2)-v_(1)^(2) = 4gr, v_(1) = sqrt(g r)`