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

Answer

A

Explanation

If the torque is not applied, then by using the principle of conservation of angular momentum,
`l_(1)omega_(1)=l_(2)omega_(2)" but "l=mK^(2)`
`therefore" "(mK_(1)^(2))omega_(1)=(mK_(2)^(2))omega_(2)`
`therefore" "(K_(1)^(2))/(K_(2)^(2))=(omega_(2))/(omega_(1))or (K_(1))/(K_(2))=sqrt((omega_(1))/(omega_(1)))`