Q1. Which of the following best reflects the principle of conservation of linear momentum?
- (a) In an isolated system, the total momentum before and after a collision remains constant, regardless of the internal forces.
- (b) The total energy in an isolated system remains zero unless acted upon by external forces.
- (c) Linear momentum can only be conserved in gravitational fields.
- (d) Linear momentum applies only to subatomic particles in a magnetic field.
Answer & solution
Answer: (a) In an isolated system, the total momentum before and after a collision remains constant, regardless of the internal forces.
When no external force acts, the internal forces between the bodies come in equal and opposite pairs (Newton's third law), so they cannot change the total momentum.
Hence m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂ for any collision, elastic or not.
Revision note — Momentum and its conservation
• Momentum p = mv; it is a vector with SI unit kg m/s (kg m s⁻¹).
• Newton's second law in its original form: force = rate of change of momentum, F = Δp/Δt; hence impulse = F × t = change in momentum.
• Law of conservation of momentum: in the absence of an external force the total momentum of a system stays constant; it follows directly from the third law.
• Applications: the recoil of a gun, rocket propulsion, a swimmer pushing water backward, and the analysis of collisions.
• In an elastic collision both momentum and kinetic energy are conserved; in an inelastic collision only momentum is conserved and some kinetic energy becomes heat or sound.
• A cricketer lowering his hands while catching, or a car's crumple zone, lengthens the time of impact and so reduces the force for the same change in momentum.
Do not mix these up
• Conservation of momentum vs conservation of energy — momentum is conserved in every collision of an isolated system; kinetic energy is conserved only in an elastic one.
• Momentum vs kinetic energy — p = mv is a vector; KE = ½mv² is a scalar. Doubling the velocity doubles the momentum but quadruples the kinetic energy.
Also asked from this topic: the scenario that best illustrates conservation of momentum (a gun recoiling when a bullet is fired); the formula for momentum (p = mv); its SI unit (kg m/s).