because point mass is "m" and rod is also of mass "m" and the rod is at rest intitially, the velocity of rod becomes 'u' both the rods i mean. now the kinetic energy 1/2 mv2 gets equal to the torque T on each rod. equate both of them.
use L= I w equation
take angular momentum L= root( 2 KE) x length of the rod
Now on RHS I= ML2 /12 + ML2/4 and w is angular speed.