A circular disc $X$ of radius $R$ is made from an iron plate of thickness $t$ and another plate $Y$ of radius $4 R$ is made from an iron plate of thickness $\frac{t}{4}$ .The ratio between moments of inertia $\frac{I_{y}}{I_{x}}$ is :

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$16$

$32$

$1$

$64$

answer is D.

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Detailed Solution

$\frac{I_{x}}{I_{y}} = \frac{\frac{m_{1} R^{2}}{2}}{\frac{m_{2} {(4 R)}^{2}}{2}} = \frac{ρ (π R^{2}) t R^{2}}{ρ π {(4 R)}^{2} \frac{t}{4} \times {(4 R)}^{2}} = \frac{1}{64}$

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