Question

If the radius of gyration of a solid disc of mass $10kg$ about an axis is $0.40m$, then the moment of inertia of the disc about that axis is :

• A. $1.6kg{m}^2$
• B. $3.2kg{m}^2$
• C. $6.4kg{m}^2$
• D. $9.5kg{m}^2$

Answer 1

The correct option is A $1.6kg{m}^2$

Given,

$M=10kg$

$K=0.40m$ radius of gyration

The radius of gyration,

$I=M{K}^2$

$K=\sqrt{\frac{I}{M}}$. . . . .(1)

The moment of inertia of disc about the axis is

$I=\frac{1}{2}M{R}^2$. . . . .(2)

Put equation (2) in (1) we get

$K=\sqrt{\frac{R^2}{2}}$

$R^2=2K^2$

The moment of inertia of disc about it's axis,

$I=\frac{1}{2}M{R}^2$

$I=\frac{1}{2}\times 10\times 2K^2$

$I=\frac{1}{2}\times 10\times 2\times 0.4\times 0.4$

$I=1.6kg{m}^2$

The correct option is A.