Two discs have same mass and thickness. Their materials are of densities $d_{1}$ and $d_{2}$ . The ratio of their moments of inertia about an axis passing through the centre and perpnedicular to the plane is

d_{1} : d_{2}

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d_{2} : d_{1}

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(\frac{d_{1}}{d_{2}})

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{(\frac{d_{2}}{d_{1}})}^{2}

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Solution

The correct option is B $d_{2} : d_{1}$
$(π R^{2} t d) = m$
$∴ R^{2} = \frac{m}{π t d}$
Now, $I = \frac{1}{2} m R^{2} = \frac{m^{2}}{2 π t d}$
or $I \propto \frac{1}{d}$
$∴ \frac{I_{1}}{I_{2}} = \frac{d_{2}}{d_{1}}$

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