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

Answer

C

Explanation

ABC is an equilateral triangle. Let `AO_|_BC`, as AO is alos a bisector of BC, i.e. AO is median of `DeltaABC.`

`I=sum_(i=1)^(i=n)m_(i)r_(i)^(2)`
`m_(1)xx0+m_(2)xx((a)/(2))^(2)+m_(3)xx((a)/(2))^(2)`
`I=(a^(2))/(4)(m_(2)+m_(3))`