Q 11-06-085JEE MainJEE Main 2024 (6 Apr, Shift 2)Medium
Three balls of masses $2\ \text{kg}$, $4\ \text{kg}$ and $6\ \text{kg}$ are placed at the midpoints of the sides of an equilateral triangle of side $2\ \text{m}$. The moment of inertia of the system about an axis through the centroid and perpendicular to the plane of the triangle will be ______ $\text{kg m}^2$.
Numerical value type. Enter your answer.
Answer: 4
The midpoint of each side is at the inradius from the centroid: $r = \dfrac{a}{2\sqrt3} = \dfrac{1}{\sqrt3}\ \text{m}$, so $r^2 = \dfrac13\ \text{m}^2$.
$$I = (2 + 4 + 6)\times\frac13 = 4\ \text{kg m}^2$$
Solution by Sreeraj P, M.Sc Physics