The moment of inertia of a solid sphere about an axis...

The moment of inertia of a solid sphere about an axis passing through centre of gravity is $\frac{1}{5} M R^{2}$; then its radius of gyration about a parallel axis at a distance $2 R$ from first axis is
(a) $5 R$
(b) $\sqrt{22 / 5} R$
(c) $\frac{5}{2} R$
(d) $\sqrt{12 / 5} R$

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Key Concepts

Radius of Gyration

This represents an effective distance from the axis of rotation at which the entire mass of the body could be assumed to be concentrated to yield the same moment of inertia. It is defined mathematically as the square root of the quotient of the moment of inertia and the total mass, and it simplifies the analysis of rotational dynamics.

Moment of Inertia

This is a physical quantity that measures an object's resistance to angular acceleration about a specified axis, depending on how its mass is distributed with respect to that axis. It is a central concept in rotational dynamics and is analogous to mass in linear motion.

Parallel Axis Theorem

This theorem allows one to calculate the moment of inertia of a body about any axis parallel to an axis through its center of mass. It states that the moment of inertia about the new axis equals the moment of inertia about the center of mass plus the product of the mass and the square of the distance between the two axes.

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