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Q.

The angular velocity of a body changes from 6 rad/sec to 54 rad/sec without applying torque but by changing moment of inertia. The ratio of the initial radius of gyration to the final radius of gyration is

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a

$\frac{1}{9}$

b

$\frac{1}{2}$

c

3

d

5

answer is D.

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Detailed Solution

$l_{1} ω_{1} = l_{1} ω_{2}$

$m k_{1}^{2} ω_{1} = m k_{2}^{2} ω_{2}$

$\frac{k_{1}}{k_{2}} = \sqrt{\frac{ω_{2}}{ω_{1}}} = \sqrt{\frac{54}{6}} = 3$

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The angular velocity of a body changes from 6 rad/sec to 54 rad/sec without applying torque but by changing moment of inertia. The ratio of the initial radius of gyration to the final radius of gyration is