Three point masses `m_1,m_2 and m_3` are located at the vertices of an equilateral triangle of length a The moment of inertia of system, about an axis along the altitude of the triangle passing through `m_1`, is

Options

A. `((m_2 + m_3)a^2)/(4)`
B. `((m_1 + m_2 + m_3)a^2)/(4)`
C. `((m_1 + m_2)a^2)/(4)`
D. `((m_1 + m_3)a^2)/(4)`

Answer

A

Explanation

AD is the altitude of `DeltaABC`. `BD = a cos 60^@ = a//2 , DC = a cos 60^@ = a//2`
A(and so `m_1`) lies upon AD.
`therefore I = (m_1 xx 0^2) + m_2 xx (a/2)^2 + m_3 xx (a/2)^2 " or " I = 0 + (m_2 xx a^2)/(4) + (m_3 xx a^2)/(4) " or " I = ((m_2 + m_3)a^2)/(4)`