An massless equlateral triangle $\inline EFG$ of side $\inline 'a'$ (As shown in the figure) has three particles of mass $\inline m$ situated at its vertices. The moment of inertia of the system about the line $\inline EX$ perpendicular to $\inline EG$ in the plane of $\inline EFG$  is $\frac{N}{20}ma^{2}$ where $\inline N$ is an integer. The value of $\inline N$ is ________. Option: 1 5 Option: 2 10 Option: 3 20 Option: 4 25

Answers (1)

The moment of inertia of the system about the line passing through EX is

$I=I_{E}+I_{F}+I_{G}$

As we know for point mass m at separation r from the axis of rotation is$I=mr^{2}$

Point masses separation from the axis of rotation at position E, F & G are 0, a/2, a respectively

$I=m(0)^{2}+m(a/2)^{2}+m(a)^{2}=\frac{5ma^{2}}{4}=\frac{25ma^{2}}{20}$

comparing with,  $\frac{N}{20}ma^{2}$

N=25

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