(c) in opposite directions with equal speeds
Explanation:
Let the velocities of two parts be v and v' and mass of each part = m. Momentum before the break = 2m*0 = 0.
Momentum after the break =mv+mv'. Since there is no external force on the body, the linear momentum will be conserved.
→mv+mv' = 0
→v = -v'
So the parts will move in opposite directions with equal speeds.