First slide

Moment of intertia

Question

Two discs have mass ratio 1 : 2 and diameter ratio 2 : 1, then find the ratio of their moments of inertia.

Moderate

A

2 : 1
B

1 : 1
C

1 : 2
D

2 : 3

Solution

Given, mass ratio of two discs,
$m_{1} : m_{2} = 1 : 2, i.e. \frac{m_{1}}{m_{2}} = \frac{1}{2}$
and diameter ratio, $\frac{d_{1}}{d_{2}} = \frac{2}{1} \Rightarrow \frac{r_{1}}{r_{2}} = \frac{2}{1}$
$∴$ Ratio of their moments of inertia,
$\frac{I_{1}}{I_{2}} = \frac{\frac{m_{1} r_{1}^{2}}{2}}{\frac{m_{2} r_{2}^{2}}{2}} = \frac{m_{1}}{m_{2}} \cdot {(\frac{r_{1}}{r_{2}})}^{2} = \frac{1}{2} {(\frac{2}{1})}^{2} = \frac{2}{1}$
$∴ I_{1} : I_{2} = 2 : 1$

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