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Question

Find the ratio of moment of inertia of a ring and a disc about an axis passing through their center and perpendicular to their plane. Both ring and disc have the same mass and same radius.

A
2:1
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B
1:4
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C
1:2
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D
4:1
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Solution

The correct option is C 1:2
Let the mass of the disc and ring =m
Let the radius of the disc and ring =r

We know, the MOI of a disc about an axis passing through the center and perpendicular to the plane is
I1=mr22 ...(I)

and MOI of a ring about an axis passing through the center and perpendicular to the plane is
I2=mr2 ...(II)

From (I) divided by (II) :
I1I2=mr2/2mr2=12
I1:I2=1:2

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