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Question

Find the ratio of radius of gyration about natural axis of a circular disk to that of a circular ring each having same mass and same radius.

A
1:1
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B
2:1
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C
1:2
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D
2:1
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Solution

The correct option is C 1:2
Let the mass and radius of the circular disk and circular ring are M and R.
We know
Radius of gyration is given by (K)
K=IM
Radius of gyration of disk Kdisc=IdiscM ...(i)
Radius of gyration of ring, Kring=IringM ....(ii)

Dividing equation (i) and (ii)
KdiscKring=IdiscIring=  MR22MR2=12
where Idisc and Iring are the moment of inertia of the circular disk and circular ring about their natural axis.

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