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21 Consider a particle moving with constant speed such that its acceleration of constant magnitude is always perpendicular to its velocity. O A It is moving in a straight line OB It is moving in a circle O CIt is moving in a parabola OD None of the above is definitely true all of the time OE I need help

21 Consider a particle moving with constant speed such that its acceleration of constant magnitude is always perpendicular to its velocity. O A It is moving in a straight line OB It is moving in a circle O CIt is moving in a parabola OD None of the above is definitely true all of the time OE I need help

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Can someone please work it out and explain it to me so I can understand 
### Understanding the Motion of a Particle with Perpendicular Acceleration and Velocity Consider a scenario where a particle is moving with a constant speed and its acceleration has a constant magnitude. Importantly, this acceleration is always perpendicular to its velocity. Based on this information, the following question is posed: **Question:** 21. Consider a particle moving with constant speed such that its acceleration of constant magnitude is always perpendicular to its velocity. **Options:** - A: It is moving in a straight line - B: It is moving in a circle - C: It is moving in a parabola - D: None of the above is definitely true all of the time - E: I need help **Analyzing the Options:** - **Option A: It is moving in a straight line** If a particle moves in a straight line with constant speed, its acceleration must be zero or parallel to its velocity. Hence, this option is incorrect because the acceleration is given as perpendicular. - **Option B: It is moving in a circle** For a particle that is moving in a circle, the acceleration, which is centripetal, is always perpendicular to the velocity and has a constant magnitude. This option is correct. - **Option C: It is moving in a parabola** In a parabolic motion, the acceleration is not always perpendicular to the velocity. The vertical component of acceleration due to gravity is constant, but this does not satisfy the given condition of always being perpendicular. - **Option D: None of the above is definitely true all of the time** This option suggests that none of the paths A, B, or C are true for the given condition, which is not correct as circular motion meets the criteria. - **Option E: I need help** This option indicates the need for further assistance in understanding the concept. **Correct Answer:** - B: It is moving in a circle This question helps in understanding the concept of motion with specific conditions on acceleration and the nature of the path followed by the particle. Analysing such scenarios is crucial in comprehending the fundamental concepts of physics, especially in dynamics and kinematics.
Transcribed Image Text:### Understanding the Motion of a Particle with Perpendicular Acceleration and Velocity Consider a scenario where a particle is moving with a constant speed and its acceleration has a constant magnitude. Importantly, this acceleration is always perpendicular to its velocity. Based on this information, the following question is posed: **Question:** 21. Consider a particle moving with constant speed such that its acceleration of constant magnitude is always perpendicular to its velocity. **Options:** - A: It is moving in a straight line - B: It is moving in a circle - C: It is moving in a parabola - D: None of the above is definitely true all of the time - E: I need help **Analyzing the Options:** - **Option A: It is moving in a straight line** If a particle moves in a straight line with constant speed, its acceleration must be zero or parallel to its velocity. Hence, this option is incorrect because the acceleration is given as perpendicular. - **Option B: It is moving in a circle** For a particle that is moving in a circle, the acceleration, which is centripetal, is always perpendicular to the velocity and has a constant magnitude. This option is correct. - **Option C: It is moving in a parabola** In a parabolic motion, the acceleration is not always perpendicular to the velocity. The vertical component of acceleration due to gravity is constant, but this does not satisfy the given condition of always being perpendicular. - **Option D: None of the above is definitely true all of the time** This option suggests that none of the paths A, B, or C are true for the given condition, which is not correct as circular motion meets the criteria. - **Option E: I need help** This option indicates the need for further assistance in understanding the concept. **Correct Answer:** - B: It is moving in a circle This question helps in understanding the concept of motion with specific conditions on acceleration and the nature of the path followed by the particle. Analysing such scenarios is crucial in comprehending the fundamental concepts of physics, especially in dynamics and kinematics.
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