The figure shows two solid discs with radius R and r respectively....

The figure shows two solid discs with radius $R$ and $r$ respectively. If mass per unit area is the same for both, what is the ratio of $MI$ of bigger disc around axis $AB$ (Which is $⊥$ 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 a moment of inertia)

The figure shows two solid discs with radius R and r respectively. If mass per unit area is the same for both, what is

Options

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

Correct answer

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

Step-by-step solution

Ratio of the moment of inertia $= \dfrac{\dfrac{1}{2}M{R}^{2}}{\dfrac{1}{4}m{r}^{2}}$

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

Practice Rotational Motion on Quantrex Academy →

More from Rotational Motion

Consider a large disk of radius R and two smaller disks, each of radius r = R/50 , lying… JEE Advanced 2026 A solid cylinder of radius R rolls without slipping with a center of mass speed v_0 =… JEE Advanced 2026 List-I shows four planar structures made of uniform solid rods each of mass m and length… JEE Advanced 2026 Passage: A uniform circular disk of radius 0.2 m and mass 1 kg is pivoted at its top… JEE Advanced 2026 Passage: A uniform circular disk of radius 0.2 m and mass 1 kg is pivoted at its top… JEE Advanced 2026 A solid cylinder having radius R and length L is slipping on a rough horizontal plane. At… JEE Main 2026 A solid sphere ( A ) of mass 5m and a spherical shell ( B ) of mass m , both having same… JEE Main 2026 A solid sphere of radius 4 cm and mass 5 kg is rotating (rotation axis is passing through… JEE Main 2026 Full Rotational Motion list All JEE Main PYQs