Four particles, each of mass 1kg are placed at four corners of a...

The formula to calculate the moment of inertia of a system of particles about a point can be written as

$I = \mathop{∑}_{i = 1}^{n}{m}_{i}{r}_{i}^{2} . . . \left(1\right)$

where, ${m}_{i}$ is the mass of the ${i}^{th}$ particle situated at a distance ${r}_{i}$ from the point.

With reference to the above diagram, it can be written that the net moment of inertia of the system of particles is

$\begin{cases}I & = & m{a}^{2} + m{a}^{2} + m ( \sqrt{2}a{)}^{2} \\ & = & 4m{a}^{2} \\ & = & 4 \times 1kg \times {\left(2m\right)}^{2} \\ & = & 16kg{m}^{2}\end{cases}$