The angular speed of a body changes from `omega_(1)` to `omega_2` without applying a torque, but due to changes in moment of inertia. The ratio of radii of gyration in the two cases is

Options

A. `omega_(2) : omega_1`
B. `sqrt(omega_(1)) : sqrt(omega_2)`
C. `sqrt(omega_(2)) : sqrt(omega_1)`
D. `omega_(1) : omega_2`

Answer

C

Explanation

As no torque is applied ,
`therefore I_(1) omega_(1) = I_(2) omega_(2) or (M k_(1)^(2)) omega_(1) = (Mk_(2)^(2)) omega_(2)`
`therefore (k_(1))/(k_(2)) = sqrt((omega_(2))/(omega_(1)))`