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Question

IA,IB and IC are the moments of inertia of a ring, semicircular ring and an arc of the same mass about the axes as shown below. Which of the following options is correct?


A
IA>IB>IC
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B
IA<IB<IC
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C
IA=IB=IC
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D
IA>IB=IC
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Solution

The correct option is C IA=IB=IC
Given that mA=mB=mC=m kg
For any arc of radius r and angle 0<θ,2π,
I=dmr2=mr2
Circular and semicircular ring are just special cases when θ=2π or π
Therefore, about the given axes,
Moment of inertia of a ring (IA)=mr2
Moment of inertia of a semicircular ring (IB)=mr2
Moment of inertia of an arc (IC)=mr2
IA=IB=IC


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