A uniform thin rod of 120 ~cm length and 1600 ~g mass is bent as shown in the figure. The moment of inertia of the bent rod about an axis passing through the point ' O ' and perpendicular to the plane of the paper is kg - m ^2 .

Step-by-step solution

There are four rods each of mass m =400 ~g =0.4 ~kg and each having a length of =30 ~cm =0.3 ~m So, we can calculate moment of inertia as follows aligned & h^2=l^2- ( l 2 )^2= 3 4 l^2 & M.I. system =( MI of I ) 2+( MI of II ) 2 & = m l^2 3 2+2 ( m l^2 12 +m h^2 ) & = 2 3 m l^2+2 ( m l^2 12 + 3 4 m l^2 ) & = 7 3 m l^2= 7 3 0.4 0.3 0.3=0.084 ~kg - m ^2 aligned