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 t/4. Then the relation between the moment of inertia IX and IY is (a) IY = 32IX (b) IY = 16IX (c) IY = IX (d) IY = 64IX

Answer: (d). I = 1/2(ρπ R² t)R² ∝ tR⁴. (IY)/(IX) = ((t/4)(4R)⁴)/(tR⁴) = 256/4 = 64 So the answer is (d) IY = 64IX.

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Moment of Inertia & Radius of Gyration

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 moment of inertia $I_X$ and $I_Y$ is

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Answer: (d)

$I = \frac{1}{2}(\rho\pi R^2 t)R^2 \propto tR^4$ .
$\frac{I_Y}{I_X} = \frac{(t/4)(4R)^4}{tR^4} = \frac{256}{4} = 64$
So the answer is (d) $I_Y = 64I_X$ .

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