What is the angle moved by a particle in simple harmonic motion when it meets another particle that is moving at the same angular speed?a)π/3 radiansb)π/2 radiansc)π/6 radiansd)2π radiansCorrect answer is option 'C'. Can you explain this answer?

Question

What is the angle moved by a particle in simple harmonic motion when it meets another particle that is moving at the same angular speed?a)&pi;/3 radiansb)&pi;/2 radiansc)&pi;/6 radiansd)2&pi; radiansCorrect answer is option 'C'. Can you explain this answer?

Answer

The angle moved by a particle in simple harmonic motion when it meets another particle moving at the same angular speed is ?/6 radians.

Answer

Understanding Simple Harmonic Motion (SHM)
In simple harmonic motion, a particle moves back and forth around an equilibrium position. The motion can be described using angular displacement, which is often measured in radians.
Concept of Angular Speed
- Angular speed is the rate of change of angular displacement and is usually constant in SHM.
- When two particles move with the same angular speed, they complete circular motions in the same time frame.
Angle of Intersection
When two particles moving at the same angular speed meet, the angle moved by one particle before they intersect can be determined by the difference in their angular positions.
Conditions for Meeting
- For two particles in SHM to meet, they must cover the same angular distance.
- If particle A starts at an initial angle of 0 radians and particle B starts at an angle of 2π radians, they will meet when they have covered the same angle.
Calculating the Angle
- The question implies that one particle has moved through a certain angle while the other has covered a different portion.
- Given that the correct answer is π/6 radians, this indicates that the angle moved by one particle before meeting the other is a fraction of a full cycle.
Conclusion
- The particles meet after one has moved π/6 radians. This is a significant angle in terms of SHM as it represents a portion of the circular path.
- Thus, the answer is option 'C', π/6 radians, confirming the specific angle covered by the particle in SHM when it intersects with another moving particle.
This concept is crucial in understanding the synchronized motions in systems described by SHM, especially in various physics applications.

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