Q.

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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a

2πρLb2+a2

b

2πρLb2a24

c

2πρLb2+a24

d

2πρLb4a44

answer is D.

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Detailed Solution

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Given length= L
Inner radius= a
Outer radius=  b
 M.I. of a shell of thickness dr  and radius r  is 
dI=ρ2πrLdrr2I= abdI= abρ2πrLdrr2=2πρL abr3dr=2πρLb4a44

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