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System of Particles and Rotational Motion

Moment of inertia

From a solid sphere of mass M and radius R, a cube of maximum

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From a solid sphere of mass $M$ and radius $R$ , a cube of maximum possible volume is cut. Moment of inertia of cube about an axis passing through its centre and perpendicular to one of its faces is
(a) $\frac{M R ^{2}}{32 2 π}$
(b) $\frac{M R ^{2}}{16 2 π}$
(c) $\frac{4 M R ^{2}}{9 3 π}$
(d) $\frac{4 M R ^{2}}{3 3 π}$

Views: 5,662 students

Updated on: Nov 29, 2022

Book:

Arihant Physics JEE Main Chapterwise Solutions (2019-2002) (Arihant)

Exam:

JEE Mains 2015

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From a solid sphere of mass

M

and radius

R

, a cube of maximum possible volume is cut. Moment of inertia of cube about an axis passing through its centre and perpendicular to one of its faces is
(a)

\frac{M R ^{2}}{32 2 π}

(b)

\frac{M R ^{2}}{16 2 π}

(c)

\frac{4 M R ^{2}}{9 3 π}

(d)

\frac{4 M R ^{2}}{3 3 π}

8 mins ago

Discuss this question LIVE

8 mins ago

Text solutionVerified

Exp. (c)
Consider the cross-sectional view of a diametric plane as shown in the adjacent diagram.
Solution Image

Cross-sectional view of the cube and sphere
Solution Image

Using geometry of the cube

PQ = 2 R = (3)

a = \frac{2 R}{3}

Volume density of the solid sphere

ρ = \frac{M}{( 4/3 ) π R ^{3}} = \frac{3}{4 π} (\frac{M}{R ^{3}})

Mass of cube

(m) = (ρ) (a)^{3}

= (\frac{3}{4 π} \times \frac{M}{R ^{3}}) [\frac{2 R}{3}]^{3} = \frac{3 M}{4 π R ^{3}} \times \frac{8 R ^{3}}{3 3} = \frac{2 M}{3 π}

Moment of inertia of the cube about given axis is

I_{Y} = \frac{m a ^{2}}{12} (a^{2} + a^{2}) = \frac{m a ^{2}}{6}

\Rightarrow I_{Y} = \frac{m a ^{2}}{6} = \frac{2 M}{3 π} \times \frac{1}{6} \times \frac{4 R ^{2}}{3} = \frac{4 M R ^{2}}{9 3 π}

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Question Text	From a solid sphere of mass $M$ and radius $R$ , a cube of maximum possible volume is cut. Moment of inertia of cube about an axis passing through its centre and perpendicular to one of its faces is (a) $\frac{M R ^{2}}{32 2 π}$ (b) $\frac{M R ^{2}}{16 2 π}$ (c) $\frac{4 M R ^{2}}{9 3 π}$ (d) $\frac{4 M R ^{2}}{3 3 π}$
Updated On	Nov 29, 2022
Topic	System of Particles and Rotational Motion
Subject	Physics
Class	Class 11
Answer Type	Text solution:1 Video solution: 4
Upvotes	555
Avg. Video Duration	16 min

Text solutionVerified

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