The figure shows two solid discs with radius R and r respectively… - Vidyadip

MCQ

The figure shows two solid discs with radius ${R}$ and ${r}$ respectively. If mass per unit area is same for both, what is the ratio of ${MI}$ of bigger disc around axis ${AB}$ (Which is $\perp$ to the plane of the disc and passing through its centre) of MI of smaller disc around one of its diameters lying on its plane? Given $'M'$ is the mass of the larger disc. ($MI$ stands for moment of inertia)

A
$2 r^{4}: R^{4}$
B
$2 {R}^{2}: {r}^{2}$
✓
$2 {R}^{4}: {r}^{4}$
D
${R}^{2}: r^{2}$

✓

Answer

Correct option: C.

$2 {R}^{4}: {r}^{4}$

c
Ratio of moment of inertia $=\frac{\frac{1}{2} MR ^{2}}{\frac{1}{4} mr ^{2}}$

$=\frac{2 \sigma \pi R^{2} R^{2}}{\sigma \pi r^{2} r^{2}}=\frac{2 R^{4}}{r^{4}}$

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