Question

Ratio of densities of material of two circular discs of same mass and thickness is $2:3$. The ratio of their moment of inertia about their natural axes is:

• A. $2:3$
• B. $3:2$
• C. $4:9$
• D. $1:1$

Answer 1

Answer: (B)

$3:2$

Let density of material 1 be $2\rho$

Let density of material 2 be $3\rho$

Since $M_1=M_2=M$

We have $\pi R_1^{2}2\rho =\pi R_2^{2}3\rho$

we get $\frac{R_1^2}{R_2^2}=\frac{3}{2}$

$\frac{I_1}{I_2}=\frac{M{R}_1^2}{M{R}_2}=\frac{3}{2}$