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

Three point masses m_(1) , m_(2), m_(3) are located at the vertices of

1.	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
Answer» `(m_(2) + m_(3)) (a^2)/(4)` `(m_(1) + m_(2) + m_(3))a^(2)` `(m_(1) + m_(2)) (a^2)/(2)` `(m_(2) + m_(3)) a^(2)` Solution :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)`