Question

Two discs have same mass and thickness. Their materials are of densities $d_1$ and $d_2$. The ratio of their moments of inertia about an axis passing through the centre and perpnedicular to the plane is

• A. $d_1:d_2$
• B. $d_2:d_1$
• C. $\left(\frac{d_1}{d_2}\right)$
• D. ${\left(\frac{d_2}{d_1}\right)}^2$

Answer 1

The correct option is B $d_2:d_1$

$\left(\pi R^{2}td\right)=m$
$\therefore R^2=\frac{m}{\pi td}$
Now, $I=\frac{1}{2}m{R}^2=\frac{m^2}{2\pi td}$
or $I\propto \frac{1}{d}$
$\therefore \frac{I_1}{I_2}=\frac{d_2}{d_1}$