A hollow cylinder of density $ρ$ of has length L inner radius a and outer radius b. its moment of inertia about the axis of the cylinder is

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$2 π ρ L (b^{2} + a^{2})$

$\frac{2 π ρ L (b^{2} - a^{2})}{4}$

$\frac{2 π ρ L (b^{2} + a^{2})}{4}$

$\frac{2 π ρ L (b^{4} - a^{4})}{4}$

answer is D.

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Detailed Solution

Given length= L
Inner radius= a
Outer radius= b
M.I. of a shell of thickness dr and radius r is
$\begin{array}{l} d I = (ρ 2 π r L d r) r^{2} \\ I =_{a}^{b} d I =_{a}^{b} ρ 2 π r L d r r^{2} = 2 π ρ L_{a}^{b} r^{3} d r = \frac{2 π ρ L (b^{4} - a^{4})}{4} \end{array}$