Selection of system in Conservation of momentum I came across a question in which a cart is moving and having sand. Suddenly the sand valve malfunctioned and the sand starts falling from the cart. So momentum of which system will remain conserved. 
 A: First, define clearly what is in The System;  it can be anything you want.  This definition is then fixed.  
If any part of this system experiences a force from outside the system in a particular direction, then the total momentum of the system in that direction is not conserved.
If all the forces on any part of the system are from other parts of the system, then the momentum of the system is conserved.
If you define the system as just the cart, and the sand falls vertically out through the bottom of the cart, then the sand exerts no horizontal force on the cart, and the momentum of this system is conserved.
If you define the system as the cart plus original amount of sand, then, as the sand falls out and hits the ground,  the ground exerts a horizontal force on part of the system, and the momentum of this system is not conserved.
Edited to address comment:
Suppose you define the system to be the cart and all the sand in it at a particular instant, $t_i$, and allow a small amount of this sand to dribble out the valve and start to fall to the ground.  Let's consider such a small amount of sand that the first part of the dribbling sand doesn't have time to reach the ground before the last part of the small amount leaves the valve
There are no external horizontal forces acting on this system, so the total momentum is conserved. The falling sand has no horizontal forces acting on it, so that part of the system has no change in momentum.  So the cart and the remaining sand (after the dribble is over) also has its momentum conserved. 
