Question

Calculate the moment of inertia of a disc of mass $M$ and radius $R$ about an axis coinciding with diameter.

• A. $\frac{M{R}^2}{3}$
• B. $\frac{M{R}^2}{4}$
• C. $\frac{M{R}^2}{2}$
• D. $M{R}^2$

Answer 1

The correct option is B $\frac{M{R}^2}{4}$

Let $X$ and $Y$ axes along two perpendicular diameters of the disc as shown.


By symmetry $I_X=I_Y$ and by perpendicular axis theorem,
$I_Z=I_X+I_Y$
And we know that for a disc $I_Z=\frac{M{R}^2}{2}$
So, we have
$\frac{M{R}^2}{2}=I_X+I_Y=2I_X$
$\therefore I_X=I_Y=\frac{M{R}^2}{4}$