Question

Four particles, each of mass $m,$are kept at the four corners of a square of edge$a.$Moment of inertia of the system about the line perpendicular to the plane of the square and passing through the centre of the square is.

• A. $3m{a}^2$
• B. $2m{a}^2$
• C. $4m{a}^2$
• D. $8m{a}^2$

Answer 1

The correct option is B $2m{a}^2$

The perpendicular distance of every particle from the given line is $\frac{a}{\sqrt{2}}$

The moment of inertia of one particle is $m(\frac{a}{\sqrt{2}}{)}^2$ = $\frac{m{a}^2}{2}$

The moment of intertia of system is therefore = $2m{a}^2$