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

Answer

D

Explanation

`I_(1)omega_(1)=I_(2)omega_(2)or,mk_(1)^(2)omega_(1)=mk_(2)^(2)omega_(2)`
`therefore (k_(1))/(k_(2))=sqrt((omega_(2))/(omega_(1)))`