Q 11-06-194JEE MainJEE Main 2020 (3 Sep, Shift 2)Medium
A massless equilateral triangle $EFG$ of side $a$ (as shown in figure) has three particles of mass $m$ situated at its vertices. The moment of inertia of the system about the line $EX$ perpendicular to $EG$ in the plane of $EFG$ is $\dfrac{N}{20}ma^{2}$ where $N$ is an integer. The value of $N$ is ______.
Numerical value type. Enter your answer.
Answer: 25
Distances from the axis $EX$: $E$ is on it ($0$), $G$ is at $a$, and $F$ (above the midpoint of $EG$) is at $\dfrac a2$.
$$I = m\cdot0 + ma^{2} + m\frac{a^{2}}{4} = \frac54ma^{2} = \frac{25}{20}ma^{2}$$
So $N = 25$.
Solution by Sreeraj P, M.Sc Physics