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}Mr_{1}^{2}}{\frac{1}{2}Mr_{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.