For a rigid body made up of N particles each of mass m, the radius of gyration, about a given axis of rotation, equals to the

Distance of any constituent particles from the axis of rotation

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Mean of the distance of the constituent particles from axis of rotation

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Root mean square value of the distance of the constituent particle from axis if rotation

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Harmonic mean of the distance of the constituent particles from the axis of rotation

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Solution

The correct option is C Root mean square value of the distance of the constituent particle from axis if rotation
As $k = \sqrt{\frac{I}{m}}$ . The moment of inertia of each N particle is given as $I = m (r_{1}^{2} + r_{2}^{2} + r_{3}^{2} + . . . . + r_{N}^{2})$ . Thus $k = \sqrt{\frac{I}{m}} = \sqrt{r_{1}^{2} + r_{2}^{2} + r_{3}^{2} + . . . . + r_{N}^{2}}$ which is the root mean square value of the distance of the constituent particle from axis if rotation.

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