Question

Two discs have same mass and thickness but are made, up of different materials having different densities. Which one of them will have larger moment of inertia?

• A. Both disc have same moment of inertia
• B. disc having less density have larger moment of inertia
• C. disc having more density have larger moment of inertia
• D. None of the above

Answer 1

Answer: (B)

Since mass of both the disc is same
$\therefore$ $\pi r_1^{2}t{\rho }_1=\pi r_2^{2}t{\rho }_2$
( $\because$ Mass = volume $\times$ density = area $\times$ thickness $\times$ density)
$\Rightarrow$ $\frac{{\rho }_1}{{\rho }_2}=\frac{r_2^2}{r_1^2}$
$\therefore$ $\frac{I_1}{I_2}=\frac{\frac{1}{2}M{r}_1^2}{\frac{1}{2}M{r}_2^2}$
$=\frac{r_1^2}{r_2^2}=\frac{{\rho }_2}{{\rho }_1}$
i.e., $I\propto \frac{1}{\rho }$
So, the disc having less density have larger moment of inertia.