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JEE Main 20245 AprilMorning Shift

Exam: JEE Main
Year: 2024
Date: 5 April
Shift: Morning Shift
Subject: Physics
Chapter: Rotational Motion

JEE Main 2024 · 5 April · Morning Shift · Physics · Rotational Motion

Ratio of radius of gyration of a hollow sphere to that of a solid...

Ratio of radius of gyration of a hollow sphere to that of a solid cylinder of equal mass, for moment of Inertia about their diameter axis

\mathrm{AB}

as shown in figure is

\sqrt{8 / x}

. The value of

x

is :

Ratio of radius of gyration of a hollow sphere to that of a solid cylinder of equal mass, for moment of Inertia about

Options

A $51$
B $34$
C $17$
D $67$

Correct answer

D. $67$

Step-by-step solution

\begin{aligned} & \mathrm{I}_{\text{sphere }}=\frac{2}{3} \mathrm{MR}^2=\mathrm{Mk}_1^2 \\ & \mathrm{I}_{\text{cylinder }}=\frac{1}{12} \mathrm{M}\left(4 \mathrm{R}^2\right)+\frac{1}{4} \mathrm{MR}^2+\mathrm{M}(2 \mathrm{R})^2 \\ & =\frac{67}{12} \mathrm{MR}^2=\mathrm{Mk}_2^2 \\ & \frac{\mathrm{k}_1}{\mathrm{k}_2}=\sqrt{\frac{2}{3} \cdot \frac{12}{67}}=\sqrt{\frac{8}{67}}\end{aligned}

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