Question

The ratio of the radii of gyration of circular disc about a tangential axis in the plane of the disc and of a circular ring of same radius about a tangential axis in the plane of the ring is _______.
1. 2 : 3
2. 2 : 1
3. \(\sqrt 5 \;:\;\sqrt 6\)
4. \(1\;:\;\sqrt 2\)

Answer 1

Correct Answer - Option 3 : \(\sqrt 5 \;:\;\sqrt 6\)

MI of a circular disc about a tangential axis in the plane of the disc,

\({I_1}\; = \;MK_1^2\; = \;\frac{5}{4}M{R^2}\)

\(\Rightarrow {K_1}\; = \;\sqrt {\frac{5}{4}} \;R\)

MI of a circular ring of the same radius about tangential axis in the plane of ring

\({I_2}\; = \;MK_2^2\; = \;\frac{3}{2}M{R^2}\)

\({K_2}\; = \;\sqrt {\frac{3}{2}} R\)

\(\frac{{{k_1}}}{{{k_2}}}\; = \;\frac{{\sqrt {\frac{5}{4}} R}}{{\sqrt {\frac{3}{2}} R}}\; = \;\frac{{\sqrt 5 }}{{\sqrt 6 }}\; = \;\sqrt 5 \;:\;\sqrt 6\)