Question

The moment of inertia of a circular of mass $M$ and radius$R$ about an axis passing through the center of mass is $10$. The moment of inertia of another circular disc of same mass and thickness but half the density about the same axis is

• A. $\frac{I_0}{8}$
• B. $\frac{I_0}{4}$
• C. $8I_0$
• D. $2I_0$

Answer 1

The correct option is D $2I_0$

$\begin{array}{c}{I}_0=\frac{M{R}^2}{2}\\ \left(\pi R^2.t\right)\rho =M\\ \left(\pi R{}^{\prime 2}.t\right){\rho }^{\prime }=M\\ \Rightarrow \frac{{\rho }^{\prime }}{\rho }={\left(\frac{R}{R^{\prime }}\right)}^2\\ \Rightarrow \frac{1}{2}={\left(\frac{R}{R^{\prime }}\right)}^2\\ R{}^{\prime 2}=2R^2\\ I=2I_0\end{array}$

$\therefore$ Option $D$ is correct.