Rotational Motion

JEE Main level, single correct, medium

53 of 280

Question 53 of 280

The figure shows two solid discs with radius RR and rr respectively. If mass per unit area is the same for both, what is the ratio of MIMI of bigger disc around axis ABAB (Which is ⊥\perp to the plane of the disc and passing through its centre) of MIMI of smaller disc around one of its diameters lying on its plane? Given MM is the mass of the larger disc.
(MIMI stands for a moment of inertia)

Show answer and solution

Answer: (D) 2R4:r42{R}^{4}:{r}^{4}

Ratio of the moment of inertia =12MR214mr2=\dfrac{\dfrac{1}{2}M{R}^{2}}{\dfrac{1}{4}m{r}^{2}}
=2σπR2R2σπr2r2=2R4r4=\dfrac{2\sigma \pi {R}^{2}{R}^{2}}{\sigma \pi {r}^{2}{r}^{2}}=\dfrac{2{R}^{4}}{{r}^{4}}

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