We will use the conservation of energy to solve this problem.
Initial Energy: there is no kinetic energy because the system starts at rest. All the energy is potential. I choose the zero of PE to be where mass one starts.
Final Conditions: the masses have moved giving new PE and also have kinetic energy, but we must also count the rotational kinetic energy of the pulley. The speeds of the two masses and the tangential velocity of the pulley are all equal because they are connected to the string. We have 49J to divide amongst PE, KE and rotational KE.
Now we have 49J - 36.75J = 12.25J to split up between translational and rotational kinetic energy.
Now we combine the equations for translational and rotational energies by adding them up and equating them to the left over energy:
