Two particles oscillate along two close parallel straight lines with the same frequency and amplitudes. They pass each other while moving in opposite directions when their displacements are half the amplitude. The mean positions of the two particles lie on a straight line perpendicular to their paths. The phase difference is:
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Question

Two particles oscillate along two close parallel straight lines with the same frequency and amplitudes. They pass each other while moving in opposite directions when their displacements are half the amplitude. The mean positions of the two particles lie on a straight line perpendicular to their paths. The phase difference is:

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G1 Physics · Accepted Answer

Step 1: Write the common displacement at crossing as x = A/2. Step 2: For one particle, sinθ = 1/2 with positive velocity, so θ₁ = π/6. Step 3: The other particle has the same displacement but opposite velocity, so θ₂ = 5π/6. Step 4: Phase difference Δφ = θ₂ − θ₁ = 5π/6 − π/6 = 2π/3. Final answer: (B) 2π/3.