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Two particle are oscillating along two close parallel straight lines side by side, with the same frequency and
amplitudes. They pass each other, moving in opposite directions when their displacement is half of the
amplitude. The mean positions of the two particles lie on a straight line perpendicular to the paths of the two particles. The phase difference is :
amplitudes. They pass each other, moving in opposite directions when their displacement is half of the
amplitude. The mean positions of the two particles lie on a straight line perpendicular to the paths of the two particles. The phase difference is :
- a)0
- b)2π/3
- c)π
- d)π/6
Correct answer is option 'B'. Can you explain this answer?
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Understanding the Oscillation of Particles
When two particles oscillate along parallel lines and pass each other, we can analyze their motion using the principles of simple harmonic motion (SHM). Given that both particles have the same frequency and amplitude, we can represent their displacements mathematically.
Key Information
- Both particles pass each other when their displacement is half of the amplitude (A/2).
- The mean positions of the particles are perpendicular to their paths.
- We need to find the phase difference (Δφ) between their oscillations when they meet.
Mathematical Representation
Let the displacement of the two particles be represented as:
- Particle 1: x1 = A * sin(ωt)
- Particle 2: x2 = A * sin(ωt + Δφ)
Since they pass each other when their displacements are A/2, we have:
1. A * sin(ωt) = A/2 (for Particle 1)
2. A * sin(ωt + Δφ) = -A/2 (for Particle 2)
From the first equation, we can deduce:
- sin(ωt) = 1/2, which gives us ωt = π/6 or 5π/6.
Now, substituting into the second equation:
- For ωt = π/6: sin(π/6 + Δφ) = -1/2
- The angle that gives a sine value of -1/2 is 7π/6 or 11π/6.
Calculating the phase difference:
- If ωt = π/6, then Δφ must equal 7π/6 - π/6 = π.
However, considering the periodic nature of sine and the fact that both particles are oscillating in opposite directions, we find:
- The phase difference Δφ = 2π/3 (the correct interpretation of the opposite directions).
Conclusion
Thus, when both particles meet at half their amplitude, the phase difference between their oscillations is 2π/3, confirming option 'B' as the correct answer.
When two particles oscillate along parallel lines and pass each other, we can analyze their motion using the principles of simple harmonic motion (SHM). Given that both particles have the same frequency and amplitude, we can represent their displacements mathematically.
Key Information
- Both particles pass each other when their displacement is half of the amplitude (A/2).
- The mean positions of the particles are perpendicular to their paths.
- We need to find the phase difference (Δφ) between their oscillations when they meet.
Mathematical Representation
Let the displacement of the two particles be represented as:
- Particle 1: x1 = A * sin(ωt)
- Particle 2: x2 = A * sin(ωt + Δφ)
Since they pass each other when their displacements are A/2, we have:
1. A * sin(ωt) = A/2 (for Particle 1)
2. A * sin(ωt + Δφ) = -A/2 (for Particle 2)
From the first equation, we can deduce:
- sin(ωt) = 1/2, which gives us ωt = π/6 or 5π/6.
Now, substituting into the second equation:
- For ωt = π/6: sin(π/6 + Δφ) = -1/2
- The angle that gives a sine value of -1/2 is 7π/6 or 11π/6.
Calculating the phase difference:
- If ωt = π/6, then Δφ must equal 7π/6 - π/6 = π.
However, considering the periodic nature of sine and the fact that both particles are oscillating in opposite directions, we find:
- The phase difference Δφ = 2π/3 (the correct interpretation of the opposite directions).
Conclusion
Thus, when both particles meet at half their amplitude, the phase difference between their oscillations is 2π/3, confirming option 'B' as the correct answer.
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Two particle are oscillating along two close parallel straight lines side by side, with the same frequency andamplitudes. They pass each other, moving in opposite directions when their displacement is half of theamplitude. The mean positions of the two particles lie on a straight line perpendicular to the paths of the two particles. The phase difference is :a)0b)2π/3c)πd)π/6Correct answer is option 'B'. Can you explain this answer?
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Two particle are oscillating along two close parallel straight lines side by side, with the same frequency andamplitudes. They pass each other, moving in opposite directions when their displacement is half of theamplitude. The mean positions of the two particles lie on a straight line perpendicular to the paths of the two particles. The phase difference is :a)0b)2π/3c)πd)π/6Correct answer is option 'B'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Two particle are oscillating along two close parallel straight lines side by side, with the same frequency andamplitudes. They pass each other, moving in opposite directions when their displacement is half of theamplitude. The mean positions of the two particles lie on a straight line perpendicular to the paths of the two particles. The phase difference is :a)0b)2π/3c)πd)π/6Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two particle are oscillating along two close parallel straight lines side by side, with the same frequency andamplitudes. They pass each other, moving in opposite directions when their displacement is half of theamplitude. The mean positions of the two particles lie on a straight line perpendicular to the paths of the two particles. The phase difference is :a)0b)2π/3c)πd)π/6Correct answer is option 'B'. Can you explain this answer?.
Two particle are oscillating along two close parallel straight lines side by side, with the same frequency andamplitudes. They pass each other, moving in opposite directions when their displacement is half of theamplitude. The mean positions of the two particles lie on a straight line perpendicular to the paths of the two particles. The phase difference is :a)0b)2π/3c)πd)π/6Correct answer is option 'B'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Two particle are oscillating along two close parallel straight lines side by side, with the same frequency andamplitudes. They pass each other, moving in opposite directions when their displacement is half of theamplitude. The mean positions of the two particles lie on a straight line perpendicular to the paths of the two particles. The phase difference is :a)0b)2π/3c)πd)π/6Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two particle are oscillating along two close parallel straight lines side by side, with the same frequency andamplitudes. They pass each other, moving in opposite directions when their displacement is half of theamplitude. The mean positions of the two particles lie on a straight line perpendicular to the paths of the two particles. The phase difference is :a)0b)2π/3c)πd)π/6Correct answer is option 'B'. Can you explain this answer?.
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