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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.


  1. 25 kg-m2
  2. 42 kg-m2
  3. 13 kg-m2
  4. 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

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