Three point masses `m_(1) , m_(2), m_(3)` are located at the vertices of an equilateral triangle of length a. The moment of inertia of systein 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)`
C. `(m_(1) + m_(2)) (a^2)/(2)`
D. `(m_(2) + m_(3)) a^(2)`

Answer

A

Explanation

Perpendicular distance of `m_(2)` and `m_(3)` from altitude of triangle = `a cos 60^(@) = (a)/(2)`
The moment of inertia of the system about the given axis is `I = m_1 xx 0^2 + m_(2) ((a)/(2))^(2) + m_(3) ((a)/(2))^(2) = (m_(2) + m_(3)) (a^(2))/(4)`