Question

Two bodies a and b of equal mass m lie on smooth frictionless horizontal table

Answer 1

Let us go by conservation of momentum.Why are we able to apply conservation of momentum here?Because there is no external force acting of it in the horizontal direction!Momentum before collision = momentum after collisionmv = M(v) + m(0)so m = M 

Where v is the velocity of of m before collision and velocity of M after collision!