Question

The angular speed of a body changes rom w1 to w2 without applying a torque but due to change in its moment of inertia. The ratio of radii of gyration in the two cases is:

• 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 1

Answer: (A)

$\sqrt{\omega_{2}}:\sqrt{\omega_{1}}$

Answer 2

$L = I\omega = MK^{2}\omega =$constant ⇒$\frac{K_{1}}{K_{2}} = \sqrt{\frac{\omega_{2}}{\omega_{1}}}$