Question

Two discs of the same material and thickness have radii $0.2m$ and $0.6m$.Their moments of inertia about their axes will be in the ratio

• A. $1:81$
• B. $1:27$
• C. $1:9$
• D. $1:3$

Answer 1

The correct option is A $1:81$

The moment of inertia of a disc about its central axis is
$I=\frac{1}{2}m{R}^2$
$\therefore$ $\frac{I_1}{I_2}=$ $\frac{\frac{1}{2}{m}_1{R}_1^2}{\frac{1}{2}{m}_2{R}_2^2}$
$=\frac{\pi R_1^{2}tp\times R_1^2}{\pi R_2^{2}tp\times R_2^2}$
$\therefore$ $\frac{I_1}{I_2}=\frac{R_1^4}{R_2^4}$
$=\frac{(0.4{)}^4}{(0.6{)}^4}=(\frac{0.1}{0.3}{)}^4=\frac{1}{81}$