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A particle is moving with constant angul...

A particle is moving with constant angular velocity along the circumference of a circle. Which of the following statements is true

A

The particle executes SHM

B

Non-periodic motion

C

The projection of the particle on any of the diameters executes SHM

D

None of the above

Text Solution

AI Generated Solution

The correct Answer is:
To solve the question regarding the motion of a particle moving with constant angular velocity along the circumference of a circle, we will analyze each of the given options step by step. ### Step 1: Understand the Motion The particle is moving along the circumference of a circle with a constant angular velocity (ω). This means that the particle completes equal angles in equal intervals of time, which is characteristic of periodic motion. **Hint:** Remember that constant angular velocity implies that the particle will return to the same position after a certain time period. ### Step 2: Analyze Option 1 Option 1 states that the particle executes simple harmonic motion (SHM). For a motion to be classified as SHM, it must be periodic and exhibit a to-and-fro motion about an equilibrium position. In this case, while the motion is periodic, it does not exhibit to-and-fro motion; it moves continuously around the circle. **Hint:** SHM requires oscillation about an equilibrium position, which is not the case here. ### Step 3: Analyze Option 2 Option 2 claims that the motion is non-periodic. Since the particle moves with constant angular velocity, it returns to its starting position after a fixed time period, indicating that the motion is periodic. **Hint:** Periodic motion is characterized by the repetition of the same motion after a fixed time interval. ### Step 4: Analyze Option 3 Option 3 states that the projection of the particle on any diameter executes simple harmonic motion. If we project the motion of the particle onto a diameter of the circle, the projection will move back and forth between two extremes as the particle moves around the circle. This projection indeed exhibits to-and-fro motion about the center, making it simple harmonic motion. **Hint:** Consider how the projection behaves as the particle moves; it should oscillate back and forth. ### Step 5: Analyze Option 4 Option 4 states that none of the above options are correct. However, we have established that option 3 is indeed correct. **Hint:** Always check if any of the previous options are valid before concluding that none are correct. ### Conclusion After analyzing all the options, we conclude that the correct statement is: **The projection of the particle on any of the diameter executes simple harmonic motion.** ### Final Answer **Option 3 is true.**
To solve the question regarding the motion of a particle moving with constant angular velocity along the circumference of a circle, we will analyze each of the given options step by step. ### Step 1: Understand the Motion The particle is moving along the circumference of a circle with a constant angular velocity (ω). This means that the particle completes equal angles in equal intervals of time, which is characteristic of periodic motion. **Hint:** Remember that constant angular velocity implies that the particle will return to the same position after a certain time period. ### Step 2: Analyze Option 1 ...
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