Radius Of Gyration

The radius of gyration $k$ is defined so that the entire mass of a body, if placed at distance $k$ from the axis, would reproduce the actual moment of inertia, through the relation $I=M{k}^2$. Solving for $k$ gives $k=\sqrt{\frac{I}{M}}$. Substituting the given values, $k=\sqrt{\frac{16}{4}}=\sqrt{4}=2\text{ m}$. The value 4 m comes from dividing $I$ by $M$ but forgetting to take the square root. The value 8 m wrongly multiplies rather than divides and also skips the square root. The value 1 m takes an incorrect square root of the ratio. This is the NCERT definition that lets a complicated mass distribution be summarised by a single effective distance from the axis. As a unit and magnitude check, $\sqrt{{\text{kg m}}^2/\text{kg}}=\sqrt{{\text{m}}^2}=\text{m}$, so the result correctly carries units of length, and a radius of gyration of 2 m is physically reasonable for the stated inertia and mass.