MPSC 2025 Prelims Paper-I · Question 53 of 100

Correct — option (2), Momentum. In any collision between two or more bodies, so long as the system is isolated from external forces (or the collision happens fast enough that external forces like gravity or friction contribute negligible impulse during the brief contact time), the total linear momentum of the system immediately before the collision equals the total linear momentum immediately after it. This follows directly from Newton's third law: during a collision the colliding bodies exert equal and opposite forces on each other for the same duration, so the impulse (and hence the momentum change) each body experiences is equal and opposite, and the net change in the system's total momentum is zero. This holds for every kind of collision — perfectly elastic, partially inelastic, and perfectly inelastic alike — which is what makes conservation of momentum the single most reliable tool for analysing collisions, unlike kinetic energy, which is conserved only in the special case of a perfectly elastic collision.

• (1)Mass — Mass of each individual object is unchanged by an ordinary mechanical collision (no material is created or destroyed), but that is simply conservation of mass in general, not a statement specific to collisions, and it is not what collision problems in mechanics are built around — momentum, not mass, is the quantity whose conservation lets you actually solve for post-collision velocities. Mass conservation also breaks down at relativistic speeds or in nuclear/particle collisions, where mass can convert to energy, unlike momentum conservation, which remains valid.
• (3)Time — Time is not a quantity that is 'conserved' by a physical interaction like a collision in the sense meant here; it is simply the independent variable along which the collision unfolds. There is no conservation law in mechanics that treats time as a conserved quantity of a system the way momentum, energy, or angular momentum are conserved.
• (4)Length — Length is a property of the colliding bodies' geometry (or the distance between them), not a dynamical quantity that a collision conserves; a collision can and often does change an object's shape or dimensions (in an inelastic collision, bodies may deform or stick together), so there is no general principle that length is preserved through a collision.

The law of conservation of momentum states that in the absence of external forces, the total linear momentum of a system of interacting bodies remains constant. In a collision, whatever forces the colliding bodies exert on each other are internal to the system and occur as equal-and-opposite action-reaction pairs (Newton's third law), so they cannot change the system's total momentum — they can only redistribute it among the individual bodies. This makes momentum conservation the foundational equation for analysing every type of collision: perfectly elastic collisions (both momentum and kinetic energy conserved), inelastic collisions (momentum conserved, some kinetic energy lost to heat, sound or deformation), and perfectly inelastic collisions (momentum conserved, colliding bodies stick together and move with a common final velocity, with maximum kinetic energy loss for the given momentum).

MPSC's physics section frequently probes the distinction between what is always conserved in a collision (momentum) versus what is conserved only under special conditions (kinetic energy, only in elastic collisions), since this distinction is the basis for every quantitative collision problem a candidate might be asked to solve. Recognising momentum as the universally conserved quantity, rather than energy or any other property, is the single most load-bearing fact in this topic.

• Total linear momentum of an isolated system is conserved in every type of collision — elastic, inelastic, and perfectly inelastic alike.
• Kinetic energy is conserved only in a perfectly elastic collision; in inelastic collisions some kinetic energy converts to heat, sound, or permanent deformation.
• Conservation of momentum in a collision follows directly from Newton's third law: the equal and opposite forces the colliding bodies exert on each other produce equal and opposite impulses, leaving total momentum unchanged.
• In a perfectly inelastic collision, the colliding bodies move together after impact with a common velocity, found using momentum conservation alone.

• Assuming kinetic energy is conserved in every collision, when it is guaranteed only for a perfectly elastic collision
• Confusing conservation of momentum (a vector law, valid for any collision) with conservation of mass (a separate, more general physical principle not specific to collisions)
• Forgetting that momentum conservation applies to the system as a whole (vector sum), not to each individual colliding body separately

MPSC's physics section frequently asks direct one-line recall questions on core conservation laws — momentum, energy, angular momentum, charge — testing whether a candidate can correctly attach each law to the physical situation (collision, rotation, closed circuit) it universally governs.

No directly related past PYQ was found.

• practice — not a real PYQ

  In a perfectly elastic collision between two bodies, which of the following is/are conserved ?

  • (a)Only momentum
  • (b)Only kinetic energy
  • (c)Both momentum and kinetic energy
  • (d)Neither momentum nor kinetic energy

  Answer(c) Both momentum and kinetic energy — a perfectly elastic collision is defined precisely by the property that both quantities are conserved, unlike an inelastic collision where only momentum is conserved.

• practice — not a real PYQ

  Conservation of momentum during a collision follows most directly from which law of motion ?

  • (a)Newton's first law
  • (b)Newton's second law
  • (c)Newton's third law
  • (d)Kepler's third law

  Answer(c) Newton's third law — the equal and opposite forces the colliding bodies exert on each other produce equal and opposite impulses, leaving the system's total momentum unchanged.