Question

The masses of two uniform discs are in the ratio $1:2$ and their diameters are in the ratio $2:1$. The ratio of their moments of inertia about the axis passing through their respective centres and perpendiculars to their planes is

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

Answer 1

The correct option is C $2:1$

Given: $m_1:m_2=1:2d_1:d_2=2:1\therefore r_1:r_2=2:1$
Therefore moment of inertia are:
$I_1=m_1{r}_1^2{I}_2=m_2{r}_2^2$
Ratio is $\frac{I_1}{I_2}=\frac{m_1{r}_1^2}{m_2{r}_2^2}=\frac{1}{2}(\frac{2}{1}{)}^2=\frac{2}{1}$