The total momentum remains constant in the absence of external forces.
Explanation
The Law of Conservation of Momentum is a fundamental principle in mechanics derived from Newton's Laws of Motion. It states that the total linear momentum of a system of particles remains constant if no net external force acts on the system. Momentum ($p$) is defined as the product of mass ($m$) and velocity ($v$).
Option Analysis
- The total momentum increases after a collision. is incorrect: In an isolated system, momentum cannot spontaneously increase. Any gain in momentum by one body must correspond to an equal and opposite loss by another body within the system.
- The total momentum decreases after a collision. is incorrect: Similarly, momentum is not lost in an isolated system. While kinetic energy may decrease in inelastic collisions (dissipated as heat or sound), the total vector momentum remains conserved.
- The total momentum remains constant in the absence of external forces. is correct: An isolated system is defined by the absence of external forces ($F_{ext} = 0$). According to Newton's Second Law, force is the rate of change of momentum ($F = \frac{dp}{dt}$). If the external force is zero, the rate of change of momentum is zero, meaning the total momentum remains constant ($p = \text{constant}$).
- The total momentum is conserved only if the colliding bodies have equal mass. is incorrect: The conservation of momentum is independent of the masses of the colliding bodies. It holds true whether the masses are equal or unequal, provided the system is isolated.
Key Takeaway: The condition for the conservation of linear momentum is solely the absence of net external forces on the system. It applies to all types of collisions (elastic and inelastic) regardless of the masses involved.