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Question

Two concentric rings, one with radius of 0.5 m and mass 1 kg and other having a radius of 1 m and mass 2 kg are placed together on a horizontal table. Find out net moment of inertia of the system, about an axis perpendicular to their plane and passing through their common centre.

A
1.75 kg-m2
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B
1.2 kg-m2
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C
2.25 kg-m2
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D
1.5 kg-m2
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Solution

The correct option is C 2.25 kg-m2
considering mass and radius of both rings
m1=1 kg
r1=0.5 m
m2=2 kg
r2=1 m

MOI of first ring about the axis XX passing through it's centre:
I1=m1r21=(1)(0.5)2
I1=0.25 kg-m2
MOI of second ring about the axis XX passing through it's centre:
I2=m2r22=(2)(1)2
I2=2 kg-m2
Net moment of inertia of system is given by:
Inet=I1+I2=0.25+2
Inet=2.25 kg-m2

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