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Moment of Inertia of a Disc

The masses of...

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

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B

1 : 2

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C

2 : 1

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D

1 : 4

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Solution

The correct option is C $2 : 1$
Given: $m_{1} : m_{2} = 1 : 2 d_{1} : d_{2} = 2 : 1 ∴ r_{1} : r_{2} = 2 : 1$
Therefore moment of inertia are:
$I_{1} = m_{1} r_{1}^{2} I_{2} = m_{2} r_{2}^{2}$
Ratio is $\frac{I_{1}}{I_{2}} = \frac{m_{1} r_{1}^{2}}{m_{2} r_{2}^{2}} = \frac{1}{2} (\frac{2}{1})^{2} = \frac{2}{1}$

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