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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 p

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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 center and perpendicular to one of its faces is:

Name: Video solution 1: 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 center and perpendicular to one of its faces is:
Uploaded: 2022-10-17T12:48:05.000Z
Duration: 25 min
Description: Video solution 1: 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 center and perpendicular to one of its faces is:

\frac{4 MR ^{2}}{9 3 π}

\frac{4 MR ^{2}}{3 3 π}

\frac{MR ^{2}}{32 2 π}

\frac{MR ^{2}}{16 2 π}

Views: 6,285 students

Updated on: Nov 12, 2022

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Michael Discussed

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 center and perpendicular to one of its faces is:

8 mins ago

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8 mins ago

Text solutionVerified

Here

a = \frac{2}{3} R

Now,

\frac{M}{M ^{'}} = \frac{\frac{4}{3} π R ^{3}}{a ^{3}}

= \frac{\frac{4}{3} π R ^{3}}{( \frac{2}{3} R ) ^{3}} = \frac{3}{2} π

M^{'} = \frac{2 M}{3 π}

Moment of inertia of the cube about the given axis,

I = \frac{M ^{'} a ^{2}}{6} = \frac{\frac{2 M}{3 π} \times ( \frac{2}{3} R ) ^{2}}{6}

I = \frac{4 MR ^{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 center and perpendicular to one of its faces is:
Updated On	Nov 12, 2022
Topic	System of Particles and Rotational Motion
Subject	Physics
Class	Class 11
Answer Type	Text solution:1 Video solution: 2
Upvotes	261
Avg. Video Duration	21 min

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 center and perpendicular to one of its faces is:

Text solutionVerified

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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 center and perpendicular to one of its faces is:

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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 center and perpendicular to one of its faces is: