Radius Of Gyration

As described in NCERT Class 11, Chapter 7 (System of Particles and Rotational Motion), the radius of gyration k is defined through the relation I = Mk², where it represents the single distance from the axis at which the entire mass of the body could be imagined to be concentrated to give the same moment of inertia. It is a convenient effective length that captures, in one number, how the mass of an arbitrarily shaped body is spread about a chosen axis, and it allows different bodies to be compared on equal footing. Rearranging the defining relation to solve for k gives k = √(I/M) = √(32/8) = √4 = 2 m. The option 4 m results from forgetting to take the square root after dividing the inertia by the mass. The option 0.5 m inverts the ratio inside the square root. The option 16 m comes from squaring the ratio rather than taking its root. A sanity check confirms that k carries units of metres, since √(kg·m²/kg) = √(m²) = m, and a radius of gyration of 2 m is fully consistent with the given moment of inertia of 32 kg·m² and mass of 8 kg.