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Question

Find the radius of gyration of a uniform circular disc of radius R=1 m and mass M=2 kg about its axis passing through the edge and normal to the disc as shown in figure.


A
12 m
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B
52 m
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C
1 m
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D
32 m
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Solution

The correct option is D 32 m
Given:
Mass of disc M=2 kg
Radius of disc R=1 m

As we know, for circular disc
Icom=MR22



Using parallel axes theorem,
I=Icom+Md2 Here, d=R
=MR22+MR2
I=32MR2
We know, Radius of gyration K=IM= 32MR2M=32×R
K=32×1 m
K=32 m
So, radius of gyration of a uniform disc about its axis passing through the edge and normal to the disc is 32 m.

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