The linear momentum of a particle is conserved if:

Correct — B, the net force on it is zero. Newton's second law is really a statement about momentum: the net force on a particle equals the rate at which its momentum changes, F = dp/dt. Read that backwards and the answer falls out. If the momentum is to stay constant, its rate of change must be nil, which means the net force must be nil — and that is exactly Newton's first law, the statement that a body left alone keeps moving as it was. The condition is on the resultant, not on the individual forces: a block sliding at steady speed with friction exactly balancing the applied pull has two forces on it and a constant momentum, because the two cancel. The same reasoning at system level is why momentum is conserved in a collision. During the impact the two bodies push on each other with equal and opposite forces, so the net force on the pair is zero however violent the internal forces are, and the total momentum before equals the total momentum after even when kinetic energy is lost. Zero net torque is the condition for a different conserved quantity altogether, and the two conditions do not imply each other — which is what makes the alternative reading of this item wrong rather than merely imprecise.

• (a)the net force on it is maximum. — The opposite of the condition. A large net force means momentum is changing as fast as it can; the phrase 'maximum' has no fixed meaning here in any case.
• (c)the net torque on it is zero. — This conserves ANGULAR momentum, not linear momentum. Torque about a point is r × F, so it vanishes whenever the force points along the line to that point even though the force is large — a planet held by the Sun's gravity has zero torque about the Sun and constant angular momentum, while its linear momentum swings round through every direction in the course of one orbit.
• (d)the net work done on it is maximum. — Work is tied to kinetic energy through the work-energy theorem, not to momentum. Even zero work would not do: a stone whirled on a string has no work done on it and yet its momentum changes direction at every instant.

Every conservation law in mechanics is paired with something that has to vanish. Linear momentum is conserved when the net external force is zero. Angular momentum is conserved when the net external torque about the chosen point is zero. Mechanical energy is conserved when no non-conservative force such as friction does work. The three are separate conditions and a system can satisfy one without the others, which is why the question of which quantity is conserved always comes back to which of the three quantities has been set to zero.

The item is a one-line definition check, and every wrong option is a near-miss from an adjacent part of the same chapter — torque from rotational motion, work from the energy section. The reliable route is to write down F = dp/dt and read it as a sentence: force is what changes momentum, so no force means no change. The torque option deserves particular attention because it is not merely a different law but a genuinely independent one. Zero force does force zero torque, but zero torque does not force zero force; the orbiting planet has one without the other. Anyone who has been taught the two conservation laws as a matched pair is exactly the candidate this option is built for. Worth knowing as a habit of mind: the conserved quantity always answers to the thing that is zero, so identify the zero first and the law follows.

• Newton's second law in momentum form is F(net) = dp/dt, so constant momentum requires zero net force.
• Zero net force giving constant momentum is Newton's first law, the law of inertia.
• Zero net torque conserves angular momentum, which is a different quantity from linear momentum.
• A central force such as gravity exerts no torque about the centre while remaining large, so angular momentum can be conserved while linear momentum is not.
• In a collision the internal forces cancel in pairs, so the total momentum of the colliding bodies is conserved even when kinetic energy is not.

• Treating zero torque and zero force as the same condition; a central force gives the first without the second.
• Thinking momentum conservation needs no forces at all — it needs the resultant to vanish, and balanced forces will do.
• Confusing the conditions for momentum conservation with those for energy conservation; a perfectly inelastic collision conserves momentum and loses kinetic energy.

As a one-line condition question like this, as a collision numerical, or as a statements item asking which quantity is conserved in a given situation.

• practice — not a real PYQ

  In a perfectly inelastic collision between two bodies on a frictionless surface, which one of the following is conserved?

  • (a)Kinetic energy only
  • (b)Linear momentum only
  • (c)Both linear momentum and kinetic energy
  • (d)Neither of the two

  Answer(b) Linear momentum only — the external force on the pair is zero so momentum is conserved, while kinetic energy is lost to deformation and heat.

• practice — not a real PYQ

  For a planet moving in an elliptical orbit around the Sun, which one of the following is conserved about the Sun?

  • (a)Linear momentum
  • (b)Angular momentum
  • (c)Kinetic energy
  • (d)Speed

  Answer(b) Angular momentum — gravity acts along the line to the Sun, so its torque about the Sun is zero; the linear momentum, speed and kinetic energy all change as the planet moves round.