The angular speed of a body changes from `omega_1` to `omega_2` without applying a torque but due to change in its moment of inertia. The ratio of radii of gyration in the two cases is :-

Options

A. `sqrt(omega_(2)): sqrt(omega_(1))`
B. `sqrt(omega)_(1)): sqrt(omega)_(2))`
C. `omega_(1) : omega_(2)`
D. `omega_(2) : omega_(1)`

Answer

A

Explanation

`I_(1) omega_(1)= I_(2) omega_(2) rArr MK_(1)^(2) omega_(1)= M K_(2)^(2) omega_(2)`
`(K_(1))/(K_(2))= sqrt((omega_(2))/(omega_(1)))`