A ring of radius 5m and linear mass density λ=0.1πkg/m is spinning about an axis passing through its COM perpendicular to its plane. Find the moment of inertia of the ring about this axis.
A
25kg-m2
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B
42kg-m2
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C
13kg-m2
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D
31kg-m2
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Solution
The correct option is A25kg-m2 Given, radius of ring (r)=5m Linear mass density (λ)=0.1πkg/m ∴ Mass of the ring (m)=λ×(circumference of the ring) =λ×2πr =0.1π×2π×5 =1kg
Moment of inertia about z axis as shown in figure Iz=mr2=1×(5)2=25kg-m2