Question

Find radius of gyration of a solid circular disc of mass M, radius R, about an axis parallel to its diameter and passing through its edge

• A. $R\frac{\sqrt{5}}{2}$
• B. $R\frac{\sqrt{3}}{2}$
• C. $\frac{R}{\sqrt{2}}$
• D. $\frac{3R}{2}$

Answer 1

The correct option is A $R\frac{\sqrt{5}}{2}$

$\begin{array}{c}\text{Moment of Inertia about an axis passing}\\ \text{through centre in the plane of the}\\ \text{disc is}\frac{M{R}^2}{4}\\ \text{about a tangent}=\frac{M{R}^2}{4}+M{R}^2\\ I=\frac{5M{R}^2}{4}\end{array}$

$\begin{array}{c}\text{Let}k\text{be radius of Gyration}\\ \begin{array}{cc}\frac{5M{R}^2}{4}& =M{k}^2\\ \Rightarrow & k=\frac{\sqrt{5}}{2}R\end{array}\\ \text{Hence option}A\text{is correct}\end{array}$