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Question

The ratio of the radii of gyration of a circular disc about a tangential axis in the plane of the disc and of a circular ring of the same radius about a tangential axis in the plane of the ring is

A
1:2
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B
1:3
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C
2:1
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D
5:6
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Solution

The correct option is D 5:6

Moment of inertia of a circular disc about the line y1

Iy1=MR24
Iy1=MR24+MR2=54MR2
(By parallel axis theorem)

K1=54R (As I=MK2)

Moment of inertia of a circular ring about the line y2

Iy2=MR22

Iy2=MR22+MR2=32MR2
K2=32R

Iy1=MK21, Iy2=MK22

K21K22=Iy1Iy2K1:K2=5:6

Hence option D is the correct answer

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