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Question

A circular ring of radius 5 m has moment of inertia of 100 kg-m2 about its natural axis. This ring is converted into a circular disc having same moment of inertia about the disc’s natural axis. What is the radius of the circular disc?

A
10 m
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B
2 m
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C
52 m
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D
5 m
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Solution

The correct option is C 52 m
Radius of ring r=5 m
Moment of inertia of ring =IRing=100 kg-m2
IRing=Mr2100=M×52
M=10025=4 kg

When the ring is converted into a disc, the mass remains same.
Mass of disc ;M=4 kg
Given: Moment of inertia of disc is also same.
Idisc=100 kg-m2
Idisc=MR22
100=4×R22R2=2004=50
R=52 m

Therefore the radius of the disc is 52 m.

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