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A frictionless circular wire of unit radius is fixed on the horizontal plane. Two point particles of unit mass start moving simultaneously from point A (θ=π/2) with identical uniform angular speeds in opposite directions, and meet again at point B (θ=-π/2). During this time, which of the following figures schematically represent the magnitude of the total linear momentum P of the system, as a function of θ? (The four graphs are shown in the figure; each runs from θ=π/2 on the left to θ=-π/2 on the right.)

Asked in Re-NEET 2026 · Discrete systems and motion of the centre of mass

• (1) Graph (1): P stays constant
• (2) Graph (2): P starts at its maximum, falls to zero midway and rises to its maximum again
• (3) Graph (3): P rises from zero to a maximum midway and falls back to zero
• (4) Graph (4): P falls in a straight line from its maximum to zero

Step-by-step solution

Why the other options are wrong

• (1) The speeds are constant but the directions are not: at A and at B the two particles move in exactly opposite directions, so the total momentum is zero there.
• (2) This is P∝|sin θ|, as if the vertical components added; in fact they cancel, and only the components along AB add, giving P=2mv cos θ.
• (4) P=2mv cos θ is not linear in θ, and it is zero, not largest, at A.

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