Net external force acting on the system along the x-axis is zero. ∴Along the x-axis Momentum is conserved ⇒mv=MV From conservation of energy Loss in GPE of particle of mass m = Gain in kinetic energy of both the masses ⇒mgh=
1
2
mv2+
1
2
MV2⇒mgh=
1
2
mv2+
1
2
M(
mv
M
)2 ⇒2gh=(1+
m
M
)v2⇒v=√
2gh
1+
m
M
hence option (A) is correct. Hence option [B] is incorrect. Since the location of center of mass does not change along the x-axis mΔx