Conservation of momentum in a collision between particles can be understood from

The correct answer is both Newton’s second and third law.

To understand how the conservation of momentum is derived during a collision between two particles, we can analyze the interaction using Newton's laws of motion:

1. Application of Newton's Third Law (Action-Reaction):
When two particles (let's call them Particle 1 and Particle 2) collide, they exert forces on each other. According to Newton's third law, the force exerted by Particle 1 on Particle 2 ($F_{12}$) is equal in magnitude and opposite in direction to the force exerted by Particle 2 on Particle 1 ($F_{21}$).
Mathematically, this is expressed as:
$F_{12}=-F_{21}$

2. Application of Newton's Second Law (Rate of Change of Momentum):
Newton's second law states that the net force acting on an object is equal to the rate of change of its linear momentum.
$F=\frac{dp}{dt}$
Applying this law to both particles during the collision interval $dt$:
For Particle 1: $F_{21}=\frac{d{p}_1}{dt}$
For Particle 2: $F_{12}=\frac{d{p}_2}{dt}$

3. Combining the Laws:
Substituting these rate-of-change expressions into the Newton's third law equation gives:
$\frac{d{p}_2}{dt}=-\frac{d{p}_1}{dt}$
Rearranging the terms:
$\frac{d{p}_1}{dt}+\frac{d{p}_2}{dt}=0$
This can be written as the derivative of the total momentum:
$\frac{d}{dt}(p_1+p_2)=0$

Since the time derivative of the total momentum of the system is zero, the total momentum ($p_1+p_2$) remains constant (conserved) throughout the collision.

Thus, the law of conservation of momentum is a direct consequence of combining both Newton's second and third laws.