Question

In an arrangement of four particles, each of mass 2 gm are situated at the coordinate points (3, 2, 0), (1, -1, 0), (0, 0, 0) and (-1, 1, 0). The moment of inertia of this arrangement about the Z-axis will be:

• A. 8 units
• B. 19 units
• C. 43 units
• D. 34 units

Answer 1

The correct option is D 34 units

The distance of each particle form the z-axis will be $\sqrt{2^2+3^2}=\sqrt{13}$,$\sqrt{1^2+(-1{)}^2}=\sqrt{2}$,$0$ and $\sqrt{1^2+1^2}=\sqrt{2}$ respectively.
Thus their moment of inertia using the relation $m{r}^2$ would be $2\times \left(\right(\sqrt{13}{)}^2+(\sqrt{2}{)}^2+(\sqrt{2}{)}^2)=34units$