Question

The moment of inertia of a circular disc of mass $M$ and radius $R$ about an axis passing through the center of mass is $I_0$. The moment of inertia of another circular disc of same mass and thickness but half the density about the same axis is,

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

Answer 1

The correct option is A $2I_0$

Mass of the disc whose density $\rho$.
$M=\rho \times \pi R^{2}t\dots \left(i\right)$
Mass of the disc whose density $\frac{\rho }{2}$.
$M=\frac{\rho }{2}\pi R_1^{2}t\dots \left(ii\right)$
From $\left(i\right)$ and $\left(ii\right)$
$R_1^2=2R^2$
Ratio of moment inertia of both discs,
$I_{\text{disc}}=\frac{1}{2}M{R}^2$
$\frac{I_1}{I_0}={\left(\frac{R_1}{R}\right)}^2=2\Rightarrow I_1=2I_0$
Final Answer: (d)