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Question

In the figure given below, four identical circular rings of mass 10 kg and radius 1 m each, are lying in the same plane. The moment of inertia of the system about an axis through point A and perpendicular to the plane of the rings is


A
440 kg-m2
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B
220 kg-m2
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C
880 kg-m2
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D
1000 kg-m2
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Solution

The correct option is C 880 kg-m2
Given,
Radius of each circular ring (r)=1 m
Mass of each circular ring (m)=10 kg

Moment of inertia of first circular ring about perpendicular axis passing through A
IA1=mr2+mr2=2mr2
(using parallel axis theorem)
=2×10(1)2=20 kg-m2
Similarly,
Moment of inertia of 2nd circular ring about axis passing through A.
IA2=mr2+m(3r)2=10mr2=100 kg-m2
Moment of inertia of 3rd circular ring about axis passing through A
IA3=mr2+m(5r)2=26mr2=260 kg-m2
Moment of inertia of 4th circular ring about axis passing through A
IA4=mr2+m(7r)2=50mr2=500 kg-m2

Therefore, total moment of inertia about axis passing through A
IA=20+100+260+500=880 kg-m2

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