Solid sphere A is rotating about an axis PQ. If the radius of the sphere is 5 cm, then its radius of gyration about PQ will be cm. The value of is ________. [2023]

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Solution

Q.
Solid sphere A is rotating about an axis PQ. If the radius of the sphere is 5 cm, then its radius of gyration about PQ will be $\sqrt{x}$ cm. The value of $x$ is ________. [2023]

Ans.
(110)

$I_{c m} = \frac{2}{5} M R^{2}$

$I_{P Q} = I_{c m} + m d^{2}$

$I_{P Q} = \frac{2}{5} m R^{2} + m {(10 cm)}^{2}$

For radius of gyration, $I_{P Q} = m k^{2}$

$\Rightarrow k^{2} = \frac{2}{5} R^{2} + {(10 cm)}^{2}$

$= \frac{2}{5} {(5)}^{2} + 100 = 10 + 100 = 110$

$\Rightarrow k = \sqrt{110} cm$

$\Rightarrow x = 110$

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