Three point masses `m_(1), m_(2)` and `m_(3)` are located at the vertices of an equilateral triangle of side `alpha`. What is the moment of inertia of the system about an axis along the altitude of the triangle passing through `m_(1)?`

Options

A. `(m_(1)+m_(2)+m_(3))a^(2)`
B. `((m_(2)+m_(3))a^(2))/6`
C. `((m_(2)+m_(3))^(2)a^(2))/2`
D. `((m_(2)+m_(3))a^(2))/4`

Answer

D

Explanation

`I=summr^(2), r_(1)=0,r_(2)=r_(3)=a/2`