A uniform solid cylinder with radius R and length L has moment of… | JEE Main 2023 (24 Jan, Shift 2)

Q110JEE Main 2023 · 24 JAN · SHIFT 2Difficult

Moment of Inertia & Radius of Gyration

A uniform solid cylinder with radius R and length L has moment of inertia I $1$ , about the axis of the cylinder. A concentric solid cylinder of radius $R' = \frac{R}{2}$ and length $L' = \frac{L}{2}$ is carved out of the original cylinder. If I $2$ is the moment of inertia of the carved out portion of the cylinder then $\frac{I_1}{I_2} =$ __________. (Both I $1$ and I $2$ are about the axis of the cylinder)

Numerical answer type. Work it out, then open the answer.

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Answer: 32

$I_1 = \frac{MR^2}{2}$
Carved mass $= M \times \frac{1}{4} \times \frac{1}{2} = \frac{M}{8}$ : $I_2 = \frac{1}{2}\frac{M}{8}\frac{R^2}{4} = \frac{MR^2}{64}$
$\frac{I_1}{I_2} = 32$

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