Three rods each of mass 1 ~kg and length 2 ~m are joined together end-to-end to form an equilateral triangle A B C . Find the moment of inertia of this system about an axis passing through its centre of mass and perpendicular to the plane of the triangle.

Step-by-step solution

Given, mass of rods, m=1 ~kg Length of rod, l=2 ~m Let moment of inertia of rod about centre of rod, I_ CM = m l^2 12 D, E and F are mid points of side A C, A B and B C, O is centroid. array ll & 30^ = O E E B 1 3 = O E l / 2 & O E= l 2 3 =O D=O F=d array By using parallel axis theorem, I=I_ CM +m d^2 and for three rods, aligned I & =3 [ m l^2 12 +m ( l 2 3 )^2 ] & =3 [ m l^2 12 + m l^2 12 ] & = m l^2 2 = 1 2^2 2 =2 ~kg - m ^2 aligned