Moment Of Inertia Of Hollow Cylinder - Practice Questions & MCQ
Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main
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MEDIUMThree hollow cylinders each of mass M and radius R are arranged as shown in the figure. If the moment of inertia of the system about an axis passing through the central line is nMR2 then find n?
Concepts Covered - 1
Moment of inertia of hollow cylinder
Let I= Moment of inertia of the hollow cylinder about its axis passing through its C.O.M
To calculate I
Consider a cylinder of mass M, radius R and length L as shown in figure
Now take an elemental ring of radius R and mass dm which is coaxial to hollow cylinder.
And Moment of inertia of elemental ring about axis of cylinder and ring is $d I=d m R^2$
So integrating Moment of inertia of such elemental rings will give I
$
\mathrm{So,} \quad I=\int d I=\int d m R^2=M R^2
$
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