Is the explosion inside the grenade an external force in the grenade problem? The momentum conservation principle assumes that there are no external forces applied to the system. We have thrown a grenade away, and it explodes at some point. Do the fragments conserve the momentum? Isn't the explosion itself an external force applied to the system?
 A: You can select arbitrary objects and consider these object as a system. There are some forces acting on these objects. Each of the forces is either internal or external: depending on if the "other object" acting on our object belongs to the system or not.
Internal forces do not affect the total momentum of our system.
Now back to the grenade example. You can decide to include only the metal parts to the system. In this case the forces produced by explosion gases are external. Total momentum of the system (that is all the metal fragments in this case) does not have to remain constant after explosion.
You can as well consider all the components of the grenade as a system. In this case forces between explosion gases and metal fragments are internal, the momentum of all these parts must remain constant. For better results explode the grenade somewhere far in space so that there is no forces from surrounding air - these are external forces and they may affect the total momentum of grenade fragments and explosion gases.
Remark: I guess the total momentum of the metal fragments of the "usual" grenade would remain almost constant after explosion. That is for some strange grenade it may happen that most of the gases goes one way, metal fragments - opposite way (so that the total momentum remains constant). But for normal grenade the effect should not be significant.
