An massless equlateral triangle EFG of side 'a' (As shown in the 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}ma^{2} where N is an integer. The value of 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 isI=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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