Mass per unit are of a circular disc of radius a depends on the distance <math> <mi>r</mi> </math> from its centre as <math> <mi>σ</mi> <mo>(</mo> <mi>r</mi> <mo>)</mo> <mo>=</mo> <mi mathvariant="normal">A</mi> <mo>+</mo> <mi mathvariant="normal">B</mi> <mi mathvariant="normal">r</mi> </math> . The moment of inertia of the disc about the axis, perpendicular to the plane and passing through its centre is: &lt;!-- [if !supportLineBreakNewLine]--&gt; &lt;!--[endif]--&gt;

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Moment of Inertia Physics System of Particles and Rotational Motion Physics Class 11th

Mass per unit are of a circular disc of radius a depends on the distance $r$ from its centre as $σ (r) = A + B r$ . The moment of inertia of the disc about the axis, perpendicular to the plane and passing through its centre is:

Option 1 -

$2 π a^{4} (\frac{A}{4} + \frac{B}{5})$

Option 2 -

$2 π a^{4} (\frac{A}{4} + \frac{a B}{5})$

Option 3 -

$2 π a^{4} (\frac{a A}{4} + \frac{B}{5})$

Option 4 -

$π a^{4} (\frac{A}{4} + \frac{a B}{5})$

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1 Answer

Answered by

alok kumar singh | Contributor-Level 10

a month ago

Correct Option - 2

Detailed Solution:

Moment of inertia of ring

$d l = {d m r}^{2}$

$I = \int_{0}^{a} ? (A + B r) 2 π r d r π r^{2}$

$= 2 π A \int_{0}^{a} ? r^{3} d r + 2 π B \int_{0}^{a} ? r^{4} d r$

$= 2 π [A \frac{a^{4}}{4} + B \frac{a^{5}}{5}]$

= 2 π a^{4} [\frac{A}{4} + \frac{B a}{5}]

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Mass per unit are of a circular disc of radius a depends on the distance $r$ from its centre as $σ (r) = A + B r$ . The moment of inertia of the disc about the axis, perpendicular to the plane and passing through its centre is:

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Mass per unit are of a circular disc of radius a depends on the distance r from its centre as σ ( r ) = A + B r . The moment of inertia of the disc about the axis, perpendicular to the plane and passing through its centre is:

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Mass per unit are of a circular disc of radius a depends on the distance $r$ from its centre as $σ (r) = A + B r$ . The moment of inertia of the disc about the axis, perpendicular to the plane and passing through its centre is: