Two discs have the same mass and thickness. Their materials are of densities $d_{1} and d_{2}$ . The ratio of their M.I about their central axis is

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d_{1} : d_{2}

d_{1}^{2} : d_{2}^{2}

d_{2} : d_{1}

d_{2}^{2} : d_{1}^{2}

answer is A.

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Detailed Solution

M_{1} R_{1}^{2} : M_{2} R_{2}^{2}

$R_{1}^{2} : R_{2}^{2}$

$M_{1} = M_{2} (∵ d = \frac{M}{v} \Rightarrow \frac{M}{A} \Rightarrow \frac{M}{π R^{2}})$

$d_{1} = \frac{M_{1}}{π R_{1}^{2}}$

$\Rightarrow R_{1}^{2} = \frac{M_{1}}{π d_{1}}$

$∥^{l y} R_{2}^{2} = \frac{M_{2}}{π d_{2}}$

$\frac{M_{1}}{π d_{1}} : \frac{M_{2}}{π d_{2}} \Rightarrow \frac{M_{1}}{d_{1}} : \frac{M_{2}}{d_{2}}$

$I_{1} : I_{2} = d_{2} : d_{1}$

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