A horizontal circular platform of radius 0.5 m and mass 0.45 kg is free to rotate about its axis. Two massless spring toy-guns, each carrying a steel ball of mass 0.05 kg are attached to the platform at a distance 0.25 m from the centre on its either sides along its diameter (see figure). Each gun simultaneously fires the balls horizontally and perpendicular to the diameter in opposite directions. After leaving the platform, the balls have horizontal speed of 9 ms^-1 with respect to the ground. The rotational speed of the platform in rad s^-1 after the balls leave the platform is

A thermodynamic system is taken from an initial state i with internal energy U_i = 100 J to the final state f along two different paths iaf and ibf, as schematically shown in the figure. The work done by the system along the paths af, ib and bf are W_af = 200 J, W_ib = 50 J and W_bf = 100 J respectively. The heat supplied to the system along the path iaf, ib and bf are Q_iaf, Q_ib and Q_bf respectively. If the internal energy of the system in the state b is U_b = 200 J and Q_iaf = 500 J, the ratio Q_bf / Q_ib is