Question

A ring of radius 5 m and linear mass density λ=0.1π kg/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.

- 25 kg-m2
- 42 kg-m2
- 13 kg-m2
- 31 kg-m2

Solution

The correct option is **A** 25 kg-m2

Given, radius of ring (r)=5 m

Linear mass density (λ)=0.1π kg/m

∴ Mass of the ring (m)=λ×(circumference of the ring)

=λ×2πr

=0.1π×2π×5

=1 kg

Moment of inertia about z axis as shown in figure

Iz=mr2=1×(5)2=25 kg-m2

Given, radius of ring (r)=5 m

Linear mass density (λ)=0.1π kg/m

∴ Mass of the ring (m)=λ×(circumference of the ring)

=λ×2πr

=0.1π×2π×5

=1 kg

Moment of inertia about z axis as shown in figure

Iz=mr2=1×(5)2=25 kg-m2

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