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  • An massless equlateral triangle of side (As shown in the figure) has three par

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)

best_answer

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

 

Posted by

avinash.dongre

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