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A proton of mass m collides elastically with a particle of unknown mass at rest. After the collision, the proton and the unknown particle are seen moving at an angle of 90° with respect to each other. The mass of unknown particle is

Asked in JEE Main Online 2018 · Momentum components in two dimensions

• (1) m
• (2) 2m
• (3) m/(√3)
• (4) /m2

Step-by-step solution

Why the other options are wrong

• (2) Comes from thinking a heavier target gives the right angle; ⃗v₁·⃗v₂=(m-M)v₂²/2m is negative for M>m, so the angle opens beyond 90°, and only M=m gives exactly 90°.
• (3) No single slip gives m/√3; the right-angle condition has no √3 in it.
• (4) Comes from thinking a lighter target gives a right angle; for M<m the dot product is positive and the angle closes below 90°.

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