In the figure given below, four identical circular rings of mass 10kg and radius 1m each, are lying in the same plane. The moment of inertia (in kg m2) of the system about an axis through point A and perpendicular to the plane of the rings is
A
880.00
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B
880
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C
880.0
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Solution
Given,
Radius of each circular ring (r)=1m
Mass of each circular ring (m)=10kg
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=20kg-m2
Similarly,
Moment of inertia of 2nd circular ring about axis passing through ′A′. IA2=mr2+m(3r)2=10mr2=100kg-m2
Moment of inertia of 3rd circular ring about axis passing through ′A′ IA3=mr2+m(5r)2=26mr2=260kg-m2
Moment of inertia of 4th circular ring about axis passing through ′A′ IA4=mr2+m(7r)2=50mr2=500kg-m2
Therefore, total moment of inertia about axis passing through ′A′ IA=20+100+260+500=880kg-m2