Q 11-06-086JEE MainJEE Main 2024 (27 Jan, Shift 1)Easy
Four particles, each of mass $1\ \text{kg}$, are placed at four corners of a square of side $2\ \text{m}$. The moment of inertia of the system about an axis perpendicular to its plane and passing through one of its vertices is ______ $\text{kg m}^2$.
Numerical value type. Enter your answer.
Answer: 16
About a corner, the other three masses are at distances $2\ \text{m}$, $2\ \text{m}$ and $2\sqrt2\ \text{m}$ (the mass on the axis contributes nothing):
$$I = 1(2^2) + 1(2^2) + 1(2\sqrt2)^2 = 4 + 4 + 8 = 16\ \text{kg m}^2$$
Solution by Sreeraj P, M.Sc Physics