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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

a
2πρLb2+a2
b
2πρLb2−a24
c
2πρLb2+a24
d
2πρLb4−a44

detailed solution

Correct option is D

Given length= LInner radius= aOuter radius=  b M.I. of a shell of thickness dr  and radius r  is dI=ρ2πrLdrr2​I= abdI= abρ2πrLdr r2=2πρL abr3dr​=2πρLb4−a44

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