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

Answer

A

Explanation

M.I. of system about the axis which passing through `m_(1)`

`I_("system")=m_(1)(0)^(2)+m_(2)((a)/(2))^(2)+m_(3)((a)/(2))^(2)`
`I_("system")=(m_(2)+m_(3))(a^(2))/(4)`.