a
(a)Let two pieces are having equal mass m and third piece have a mass of \(3m\).
According to law of conservation of linear momentum. Since the initial momentum of the system was zero, therefore final momentum of the system must be zero i.e. the resultant of momentum of two pieces must be equal to the momentum of third piece. We know that if two particle possesses same momentum and angle in between them is \(90°\) then resultant will be given by \(P\sqrt 2 = mv\sqrt 2 = m30\sqrt 2 \)
Let the velocity of mass \(3m\) is \(V\). So \(3mV = 30m\sqrt 2 \)
 \(V = 10\sqrt 2 \) and angle \(135°\) from either.
(as it is clear from the figure)