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A circular disc X of radius R is made from an iron plate of thickness t, and another disc Y of radius 4R is made from an iron plate of thickness $\frac{t}{4}$ , then the relation between the moments of inertia $I_{X} and I_{Y}$ is

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$I_{Y} = 16 I_{X}$

$I_{Y} = I_{X}$

$I_{Y} = 64 I_{X}$

$I_{Y} = 32 I_{X}$

answer is C.

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Detailed Solution

$Let ρ be the density of iron .$

Then the mass of X $M_{X} = {πR}^{2} tρ$

The mass of Y $M_{Y} = π {(4 R)}^{2} \frac{t}{4} ρ = 4 M_{X}$

$I_{X} = \frac{1}{2} M_{X} R^{2} I_{Y} = \frac{1}{2} (4 M_{X}) {(4 R)}^{2} = 64 I_{X}$

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