Question 31 of 280

Four particles, each of mass $1kg$ are placed at four corners of a square of side $2m$. The moment of inertia of the system about an axis perpendicular to its plane and passing through one of its vertex is ______kg{m}^{2}.

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Answer: 16

The formula to calculate the moment of inertia of a system of particles about a point can be written as
$I=\sum _{i=1}^{n}{m}_{i}{r}_{i}^{2}...\left(1\right)$
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
$\begin{matrix}I & = & m{a}^{2}+m{a}^{2}+m(\sqrt{2}a{)}^{2} \\ & = & 4m{a}^{2} \\ & = & 4\times 1kg\times {\left(2m\right)}^{2} \\ & = & 16kg{m}^{2}\end{matrix}$