Question

Ratio of moment of inertia of two rings is $2 : 1$ and ratio of their diameters is $2 : 1$. Then, the ratio of their mass will be

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

Answer 1

Answer: (B)

Moment of inertia of ring $I=m r^{2} \frac{I_{1}}{I_{2}}=\left(\frac{m_{1}}{m_{2}}\right)\left(\frac{r_{1}}{r_{2}}\right)^{2}$
Given, $\frac{I_{1}}{I_{2}}=\frac{2}{1}$
And $\frac{r_{1}}{r_{2}}=\frac{2}{1}$
$\frac{2}{1}=\left(\frac{m_{1}}{m_{2}}\right)\left(\frac{2}{1}\right)^{2}$
Hence, $\frac{m_{1}}{m_{2}}=1: 2$