Three point-mases `m_(1),m_(2)andm_(3)` are located at the vertices of an equilateral triangle of side a. 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))(a^(2))/(4)`
B. `(m_(1)+m_(2)+m_(3))(a^(2))/(4)`
C. `(m_(2)+m_(3))(a^(2))/(4)`
D. `(m_(1)+m_(3))(a^(2))/(4)`

Answer

C

Explanation

`I_(AD)=m_(1)xx0^(2)+m_(2)xxBD^(2)+m_(3)xxCD^(2)`
`=0+m_(2)((a)/(2))^(2)+m_(3)((a)/(2))^(2)`
`I_(AD)=(m_(2)+m_(3))(a^(2))/(4)`