If the radius of curvature of the path of two particles of same masses are in the ratio `1 : 2`, then in order to have same centripetal force, their velocity, should be in the ratio of

Options

A. `1:4`
B. `4:1`
C. `sqrt(2):1`
D. `1:sqrt(2)`

Answer

D

Explanation

`F = (mv^(2))/r rArr r = (mv^(2))/F` If m and F are constant.
`r prop v^(2) rArr v prop sqrt( r) rArr v_(1)/v_(2) = sqrt(r_(1)/r_(2)) = sqrt(1/2)`