NEET Exam > NEET Questions > A particle moves so that its position vector ...
Start Learning for Free
A particle moves so that its position vector is given by r = cosωtx + sinωty. Where ω is a constant.
Which of the following is true?
- a)Velocity is perpendicular to r and acceleration is directed away from the origin.
- b)Velocity and acceleration both are perpendicular to r
- c)Velocity is acceleration both are parallel to r
- d)Velocity is perpendicular to r and acceleration is directed towards the origin.
Correct answer is option 'D'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
A particle moves so that its position vector is given by r =cosωt...
Explanation:
Given Position Vector:
The position vector of the particle is given by r = costx + sinty, where t is a constant.
Velocity and Acceleration:
- The velocity of the particle can be found by taking the derivative of the position vector with respect to time.
- The velocity vector v = (-sin(t)x + cos(t)y) = -r'
- The acceleration of the particle can be found by taking the derivative of the velocity vector with respect to time.
- The acceleration vector a = (-cos(t)x - sin(t)y) = -v'
Relationship between Velocity and Acceleration:
- The velocity and acceleration vectors are perpendicular to each other if the dot product of the two vectors is zero.
- v.a = (-sin(t)x + cos(t)y) . (-cos(t)x - sin(t)y) = 0
- This implies that the velocity is perpendicular to the acceleration vector.
Direction of Velocity and Acceleration:
- Since the velocity vector v = -r' and acceleration vector a = -v', the velocity is perpendicular to the position vector r.
- Moreover, the acceleration is in the opposite direction of the velocity, which means it is directed towards the origin.
- Therefore, the correct option is D) Velocity is perpendicular to r and acceleration is directed towards the origin.
Given Position Vector:
The position vector of the particle is given by r = costx + sinty, where t is a constant.
Velocity and Acceleration:
- The velocity of the particle can be found by taking the derivative of the position vector with respect to time.
- The velocity vector v = (-sin(t)x + cos(t)y) = -r'
- The acceleration of the particle can be found by taking the derivative of the velocity vector with respect to time.
- The acceleration vector a = (-cos(t)x - sin(t)y) = -v'
Relationship between Velocity and Acceleration:
- The velocity and acceleration vectors are perpendicular to each other if the dot product of the two vectors is zero.
- v.a = (-sin(t)x + cos(t)y) . (-cos(t)x - sin(t)y) = 0
- This implies that the velocity is perpendicular to the acceleration vector.
Direction of Velocity and Acceleration:
- Since the velocity vector v = -r' and acceleration vector a = -v', the velocity is perpendicular to the position vector r.
- Moreover, the acceleration is in the opposite direction of the velocity, which means it is directed towards the origin.
- Therefore, the correct option is D) Velocity is perpendicular to r and acceleration is directed towards the origin.
Free Test
FREE
| Start Free Test |
Community Answer
A particle moves so that its position vector is given by r =cosωt...
The equation represents UCM hence d
Attention NEET Students!
To make sure you are not studying endlessly, EduRev has designed NEET study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in NEET.
|
Explore Courses for NEET exam
|
|
Similar NEET Doubts
Top Courses for NEETView all
A particle moves so that its position vector is given by r =cosωtx +sinωty.Where ωis a constant.Which of the following is true?a)Velocity is perpendicular to rand acceleration is directed away from the origin.b)Velocity and acceleration both are perpendicular to rc)Velocity is acceleration both are parallel to rd)Velocity is perpendicular to rand acceleration is directed towards the origin.Correct answer is option 'D'. Can you explain this answer?
Question Description
A particle moves so that its position vector is given by r =cosωtx +sinωty.Where ωis a constant.Which of the following is true?a)Velocity is perpendicular to rand acceleration is directed away from the origin.b)Velocity and acceleration both are perpendicular to rc)Velocity is acceleration both are parallel to rd)Velocity is perpendicular to rand acceleration is directed towards the origin.Correct answer is option 'D'. 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 A particle moves so that its position vector is given by r =cosωtx +sinωty.Where ωis a constant.Which of the following is true?a)Velocity is perpendicular to rand acceleration is directed away from the origin.b)Velocity and acceleration both are perpendicular to rc)Velocity is acceleration both are parallel to rd)Velocity is perpendicular to rand acceleration is directed towards the origin.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle moves so that its position vector is given by r =cosωtx +sinωty.Where ωis a constant.Which of the following is true?a)Velocity is perpendicular to rand acceleration is directed away from the origin.b)Velocity and acceleration both are perpendicular to rc)Velocity is acceleration both are parallel to rd)Velocity is perpendicular to rand acceleration is directed towards the origin.Correct answer is option 'D'. Can you explain this answer?.
A particle moves so that its position vector is given by r =cosωtx +sinωty.Where ωis a constant.Which of the following is true?a)Velocity is perpendicular to rand acceleration is directed away from the origin.b)Velocity and acceleration both are perpendicular to rc)Velocity is acceleration both are parallel to rd)Velocity is perpendicular to rand acceleration is directed towards the origin.Correct answer is option 'D'. 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 A particle moves so that its position vector is given by r =cosωtx +sinωty.Where ωis a constant.Which of the following is true?a)Velocity is perpendicular to rand acceleration is directed away from the origin.b)Velocity and acceleration both are perpendicular to rc)Velocity is acceleration both are parallel to rd)Velocity is perpendicular to rand acceleration is directed towards the origin.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle moves so that its position vector is given by r =cosωtx +sinωty.Where ωis a constant.Which of the following is true?a)Velocity is perpendicular to rand acceleration is directed away from the origin.b)Velocity and acceleration both are perpendicular to rc)Velocity is acceleration both are parallel to rd)Velocity is perpendicular to rand acceleration is directed towards the origin.Correct answer is option 'D'. Can you explain this answer?.
Solutions for A particle moves so that its position vector is given by r =cosωtx +sinωty.Where ωis a constant.Which of the following is true?a)Velocity is perpendicular to rand acceleration is directed away from the origin.b)Velocity and acceleration both are perpendicular to rc)Velocity is acceleration both are parallel to rd)Velocity is perpendicular to rand acceleration is directed towards the origin.Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for NEET.
Download more important topics, notes, lectures and mock test series for NEET Exam by signing up for free.
Here you can find the meaning of A particle moves so that its position vector is given by r =cosωtx +sinωty.Where ωis a constant.Which of the following is true?a)Velocity is perpendicular to rand acceleration is directed away from the origin.b)Velocity and acceleration both are perpendicular to rc)Velocity is acceleration both are parallel to rd)Velocity is perpendicular to rand acceleration is directed towards the origin.Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
A particle moves so that its position vector is given by r =cosωtx +sinωty.Where ωis a constant.Which of the following is true?a)Velocity is perpendicular to rand acceleration is directed away from the origin.b)Velocity and acceleration both are perpendicular to rc)Velocity is acceleration both are parallel to rd)Velocity is perpendicular to rand acceleration is directed towards the origin.Correct answer is option 'D'. Can you explain this answer?, a detailed solution for A particle moves so that its position vector is given by r =cosωtx +sinωty.Where ωis a constant.Which of the following is true?a)Velocity is perpendicular to rand acceleration is directed away from the origin.b)Velocity and acceleration both are perpendicular to rc)Velocity is acceleration both are parallel to rd)Velocity is perpendicular to rand acceleration is directed towards the origin.Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of A particle moves so that its position vector is given by r =cosωtx +sinωty.Where ωis a constant.Which of the following is true?a)Velocity is perpendicular to rand acceleration is directed away from the origin.b)Velocity and acceleration both are perpendicular to rc)Velocity is acceleration both are parallel to rd)Velocity is perpendicular to rand acceleration is directed towards the origin.Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A particle moves so that its position vector is given by r =cosωtx +sinωty.Where ωis a constant.Which of the following is true?a)Velocity is perpendicular to rand acceleration is directed away from the origin.b)Velocity and acceleration both are perpendicular to rc)Velocity is acceleration both are parallel to rd)Velocity is perpendicular to rand acceleration is directed towards the origin.Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice NEET tests.
|
|
Explore Courses for NEET exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup