First slide

Moment of intertia

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 :

Moderate

A

2:1
B

$\sqrt{5} : \sqrt{6}$
C

2:3
D

$1 : \sqrt{2}$

Solution

$\begin{array}{l} I_{disc} = \frac{{MR}^{2}}{4} + M (R)^{2} = \frac{5}{4} {MR}^{2} \\ and I_{ring} = \frac{{MR}^{2}}{2} + {MR}^{2} = \frac{3}{2} {MR}^{2} \\ \Rightarrow K_{disc} = \frac{\sqrt{5}}{2} R and K_{ring} = \sqrt{\frac{3}{2}} R \\ \Rightarrow \frac{K_{disc}}{K_{ring}} = \sqrt{\frac{5}{6}} \end{array}$

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