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Question

Calculate the moment of Inertia of a solid cylinder of mass 'M' and radius R about its Axis(as shown)?


A

MR2

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B

MR24

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C

MR22

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D

MR23

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Solution

The correct option is C

MR22


Draw two cylindrical surfaces of radii x and x+dx{as shown in figure}. Consider the part of the cylinder

in between the two surfaces given length of the cylinder = h

Mass per unit volume of the cylinder = MπR2h

Then the mass of hollow cylinder cinsidered = dm

= MπR2h× 2π xdx × h

= 2MR2 × xdx ..........(i)

As its radius is x, its moment of Inertia about the given axis = dm.x2

I = R0 x2 dm

From (1)

I = R02MR2x3 dx = MR22

Note: It does not depends upon the length (i.e. h) of the cylinder.


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