Strict application of conservation of linear momentum I got a question that goes like this:-
The principle of conservation of linear momentum can be strictly applied during a collision
between two particles provided the time of impact is:
A) Extremely Large
B) Extremely small
C) Moderately Small
D) Depends on particular case

The question is, why should conservation of linear momentum even depend on the time of impact. Shouldn't it be applied strictly in all the cases?
The answer can be found on several pages but with no valid explanation or proof.
 A: This is probably based on the definition of an impulsive force. While considering collisions we take into account the impulsive force which is responsible for the change in momentum.
$$\int_{t_1}^{t_2} F\cdot dt=m\ dv$$
Since the impulsive force acts for a very small period of time.
A: 
why should conservation of linear momentum even depend on the time of impact.

It does not.  In physics theories laws are axioms distilled from observations , to use on the mathematics of the model in order to fit and predict data and observations. In the case of momentum conservation:

Newton used the third law to derive the law of conservation of momentum;from a deeper perspective, however, conservation of momentum is the more fundamental idea (derived via Noether's theorem from Galilean invariance), and holds in cases where Newton's third law appears to fail, for instance when force fields as well as particles carry momentum, and in quantum mechanics.

If the interaction is complicated one has to go into the details of the interaction, always axiomatically assuming that energy momentum and angular momentum conservation are laws always obeyed. Using the conservation laws  is one of the ways that a number of neutral  particles have been found, the neutrino as a first example.
