The correct option is D opposite directions with equal velocities.
Let the mass of the bomb be M.
∴The masses of two equal fragments of the bomb is M2 each.
Let U be the initial velocity of the bomb and v1 and v2 be the velocity of the fragments after explosion.
As there is no external force applied in this case,
∴ momentum before explosion = momentum after explosion.
i.e, MU=M2 v1+M2 v2
As bomb was at rest initially, MU=0
we have, M2 v1+M2 v2 will also be equal to zero.
∴ M2 v1+M2 v2=0
M2 v1=−M2 v2
⇒ v1=−v2
This means the fragments will move in opposite directions with equal velocity.