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Moment of Inertia of a Disc

Two circular ...

Question

Two circular discs with masses $M_{1}$ and $M_{2}$ and diameter $D_{1}$ and $D_{2}$ respectively are designed to have the same moment of inertia about the axis along the diameter of the discs.If $M_{1} : M_{2} = 9 : 4$ then the ratio of their area $A_{1} : A_{2}$ is

A

3 : 2

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B

2 : 3

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C

4 : 9

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D

81 : 16

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Solution

The correct option is A 4 : 9
Moment of inertia $I = \frac{1}{2} M R^{2}$
$⟹$ $I = \frac{M A}{2 π}$ where $A = π R^{2}$
Given : $I_{1} = I_{2}$
$∴$ $M_{1} A_{1} = M_{2} A_{2}$
$∴$ $A_{1} : A_{2} = M_{2} : M_{1} = 4 : 9$

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