Question

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 $\frac{N}{20}m{a}^2$ where $N$ is an integer. The value of $N$ is .

Answer 1

Moment of inertia of the system about axis $EX$.
$I=I_E+I_F+I_G$

$\Rightarrow I=m(r_E{)}^2+m(r_F{)}^2+m(r_G{)}^2$

$\Rightarrow I=m\times 0^2+m{\left(\frac{a}{2}\right)}^2+m{a}^2=\frac{5}{4}m{a}^2$

$\Rightarrow I=\frac{25}{20}m{a}^2$

$\therefore N=25$

Hence, $25$ is the correct answer.