Question

Two disc have their moments of inertia in the ratio $1:2$ and their diameters are in ratio $2:1$. The ratio of their masses will be

• A. $1:4$
• B. $1:8$
• C. $3:4$
• D. $5:4$

Answer 1

Answer: (B)

No specific axis of rotation is given so we use relation
$I=m{r}^2$
$\Rightarrow \therefore \frac{M_1}{M_2}=\frac{I_1}{R_1^2}\times \frac{R_2^2}{I_2}$
$\therefore \frac{M_1}{M_2}=\frac{I_1}{I_2}\times {\left(\frac{R_2}{R_1}\right)}^2$
$=\frac{1}{2}\times {\left(\frac{1}{2}\right)}^2=\frac{1}{8}$