Question

Two discs have same mass and thickness. Their materials are of densities ${\pi }_1$ and ${\pi }_2$. The ratio of their moment of inertia about central axis will be

• A. ${\pi }_1:{\pi }_2$
• B. ${\pi }_1{\pi }_2:1$
• C. $1:{\pi }_1{\pi }_2$
• D. ${\pi }_2:{\pi }_1$

Answer 1

The correct option is D ${\pi }_2:{\pi }_1$

Mass of disc= material density x (area x thickness)

As mass and thickness of both discs is same

$\therefore {\pi }_1\left(\pi {r_1}^2\right)={\pi }_2\left(\pi {r_2}^2\right)\frac{{r_1}^2}{{r_1}^2}=\frac{{\pi }_2}{{\pi }_1}$

Moment of Inertia of disc = $m{r}^2/2$

Moment of Inertia of disc 1, $I_1=m{r_1}^2/2$

Moment of Inertia of disc 2, $I_2=m{r_2}^2/2$

$\therefore \frac{I_1}{I_2}=\frac{{r_1}^2}{{r_2}^2}=\frac{{\pi }_2}{{\pi }_1}$