JEE Exam > JEE Questions > At some instant, a particle is moving along ...
Start Learning for Free
At some instant, a particle is moving along a straight line 2x - 3y = 2 and its co-ordinates on that line are (4, 2). Now, at another instant, the same particle is moving along a straight line 3x + 4y = 7 and its co-ordinates are (1, 1). Find the co-ordinates of that axis about which it is in pure rotation.
- a)30/17 , 35/17
- b)50/17 , 61/17
- c)8/9 , 16/9
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
At some instant, a particle is moving along a straight line 2x - 3y =...
To find the coordinates of the axis about which the particle is in pure rotation, we need to find the center of rotation and the radius of rotation.
1. Finding the Center of Rotation:
Since the particle is moving along a straight line, the center of rotation lies on the intersection of the two lines.
We have the equations:
2x - 3y = 2 ...(1)
3x + 4y = 7 ...(2)
To find the intersection point, we solve these two equations simultaneously.
Multiplying equation (1) by 3 and equation (2) by 2, we get:
6x - 9y = 6 ...(3)
6x + 8y = 14 ...(4)
Subtracting equation (3) from equation (4), we eliminate x:
17y = 8
y = 8/17
Substituting the value of y in equation (1), we find:
2x - 3(8/17) = 2
2x = 2 + (24/17)
2x = (34/17) + (24/17)
2x = 58/17
x = 29/17
Therefore, the center of rotation is (29/17, 8/17).
2. Finding the Radius of Rotation:
To find the radius of rotation, we need to calculate the distance between the center of rotation and any point on the line.
Let's take the point (4, 2) which lies on the line 2x - 3y = 2. Using the distance formula, the distance between the center of rotation and (4, 2) is given by:
√[(29/17 - 4)^2 + (8/17 - 2)^2]
Simplifying this, we get:
√[(29/17 - 68/17)^2 + (8/17 - 34/17)^2]
√[(-39/17)^2 + (-26/17)^2]
√[(1521/289) + (676/289)]
√(2197/289)
√(2197)/√(289)
47/17
Therefore, the radius of rotation is 47/17.
Hence, the coordinates of the axis about which the particle is in pure rotation are (29/17, 8/17) and the radius of rotation is 47/17.
The correct answer is option 'B': 50/17, 61/17.
1. Finding the Center of Rotation:
Since the particle is moving along a straight line, the center of rotation lies on the intersection of the two lines.
We have the equations:
2x - 3y = 2 ...(1)
3x + 4y = 7 ...(2)
To find the intersection point, we solve these two equations simultaneously.
Multiplying equation (1) by 3 and equation (2) by 2, we get:
6x - 9y = 6 ...(3)
6x + 8y = 14 ...(4)
Subtracting equation (3) from equation (4), we eliminate x:
17y = 8
y = 8/17
Substituting the value of y in equation (1), we find:
2x - 3(8/17) = 2
2x = 2 + (24/17)
2x = (34/17) + (24/17)
2x = 58/17
x = 29/17
Therefore, the center of rotation is (29/17, 8/17).
2. Finding the Radius of Rotation:
To find the radius of rotation, we need to calculate the distance between the center of rotation and any point on the line.
Let's take the point (4, 2) which lies on the line 2x - 3y = 2. Using the distance formula, the distance between the center of rotation and (4, 2) is given by:
√[(29/17 - 4)^2 + (8/17 - 2)^2]
Simplifying this, we get:
√[(29/17 - 68/17)^2 + (8/17 - 34/17)^2]
√[(-39/17)^2 + (-26/17)^2]
√[(1521/289) + (676/289)]
√(2197/289)
√(2197)/√(289)
47/17
Therefore, the radius of rotation is 47/17.
Hence, the coordinates of the axis about which the particle is in pure rotation are (29/17, 8/17) and the radius of rotation is 47/17.
The correct answer is option 'B': 50/17, 61/17.
Free Test
FREE
| Start Free Test |
Community Answer
At some instant, a particle is moving along a straight line 2x - 3y =...
Axis of pure rotation will be on the perpendicular line of both the straight lines.
Intersection of these two lines passing through (4, 2) and (1, 1) will be the co-ordinates of the axis of pure rotation.
The line given by 2y + 3x = 16 is perpendicular to 2x - 3y = 2 and the line given by 3y - 4x = -1 is perpendicular to 3x + 4y = 7.
On solving 2y + 3x = 16 and 3y - 4x = -1, we get
x = 50/17 and y = 61/17
Attention JEE Students!
To make sure you are not studying endlessly, EduRev has designed JEE study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in JEE.
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
At some instant, a particle is moving along a straight line 2x - 3y = 2 and its co-ordinates on that line are (4, 2). Now, at another instant, the same particle is moving along a straight line 3x + 4y = 7 and its co-ordinates are (1, 1). Find the co-ordinates of that axis about which it is in pure rotation.a)30/17 , 35/17b)50/17 , 61/17c)8/9 , 16/9d)None of theseCorrect answer is option 'B'. Can you explain this answer?
Question Description
At some instant, a particle is moving along a straight line 2x - 3y = 2 and its co-ordinates on that line are (4, 2). Now, at another instant, the same particle is moving along a straight line 3x + 4y = 7 and its co-ordinates are (1, 1). Find the co-ordinates of that axis about which it is in pure rotation.a)30/17 , 35/17b)50/17 , 61/17c)8/9 , 16/9d)None of theseCorrect answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about At some instant, a particle is moving along a straight line 2x - 3y = 2 and its co-ordinates on that line are (4, 2). Now, at another instant, the same particle is moving along a straight line 3x + 4y = 7 and its co-ordinates are (1, 1). Find the co-ordinates of that axis about which it is in pure rotation.a)30/17 , 35/17b)50/17 , 61/17c)8/9 , 16/9d)None of theseCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for At some instant, a particle is moving along a straight line 2x - 3y = 2 and its co-ordinates on that line are (4, 2). Now, at another instant, the same particle is moving along a straight line 3x + 4y = 7 and its co-ordinates are (1, 1). Find the co-ordinates of that axis about which it is in pure rotation.a)30/17 , 35/17b)50/17 , 61/17c)8/9 , 16/9d)None of theseCorrect answer is option 'B'. Can you explain this answer?.
At some instant, a particle is moving along a straight line 2x - 3y = 2 and its co-ordinates on that line are (4, 2). Now, at another instant, the same particle is moving along a straight line 3x + 4y = 7 and its co-ordinates are (1, 1). Find the co-ordinates of that axis about which it is in pure rotation.a)30/17 , 35/17b)50/17 , 61/17c)8/9 , 16/9d)None of theseCorrect answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about At some instant, a particle is moving along a straight line 2x - 3y = 2 and its co-ordinates on that line are (4, 2). Now, at another instant, the same particle is moving along a straight line 3x + 4y = 7 and its co-ordinates are (1, 1). Find the co-ordinates of that axis about which it is in pure rotation.a)30/17 , 35/17b)50/17 , 61/17c)8/9 , 16/9d)None of theseCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for At some instant, a particle is moving along a straight line 2x - 3y = 2 and its co-ordinates on that line are (4, 2). Now, at another instant, the same particle is moving along a straight line 3x + 4y = 7 and its co-ordinates are (1, 1). Find the co-ordinates of that axis about which it is in pure rotation.a)30/17 , 35/17b)50/17 , 61/17c)8/9 , 16/9d)None of theseCorrect answer is option 'B'. Can you explain this answer?.
Solutions for At some instant, a particle is moving along a straight line 2x - 3y = 2 and its co-ordinates on that line are (4, 2). Now, at another instant, the same particle is moving along a straight line 3x + 4y = 7 and its co-ordinates are (1, 1). Find the co-ordinates of that axis about which it is in pure rotation.a)30/17 , 35/17b)50/17 , 61/17c)8/9 , 16/9d)None of theseCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of At some instant, a particle is moving along a straight line 2x - 3y = 2 and its co-ordinates on that line are (4, 2). Now, at another instant, the same particle is moving along a straight line 3x + 4y = 7 and its co-ordinates are (1, 1). Find the co-ordinates of that axis about which it is in pure rotation.a)30/17 , 35/17b)50/17 , 61/17c)8/9 , 16/9d)None of theseCorrect answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
At some instant, a particle is moving along a straight line 2x - 3y = 2 and its co-ordinates on that line are (4, 2). Now, at another instant, the same particle is moving along a straight line 3x + 4y = 7 and its co-ordinates are (1, 1). Find the co-ordinates of that axis about which it is in pure rotation.a)30/17 , 35/17b)50/17 , 61/17c)8/9 , 16/9d)None of theseCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for At some instant, a particle is moving along a straight line 2x - 3y = 2 and its co-ordinates on that line are (4, 2). Now, at another instant, the same particle is moving along a straight line 3x + 4y = 7 and its co-ordinates are (1, 1). Find the co-ordinates of that axis about which it is in pure rotation.a)30/17 , 35/17b)50/17 , 61/17c)8/9 , 16/9d)None of theseCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of At some instant, a particle is moving along a straight line 2x - 3y = 2 and its co-ordinates on that line are (4, 2). Now, at another instant, the same particle is moving along a straight line 3x + 4y = 7 and its co-ordinates are (1, 1). Find the co-ordinates of that axis about which it is in pure rotation.a)30/17 , 35/17b)50/17 , 61/17c)8/9 , 16/9d)None of theseCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice At some instant, a particle is moving along a straight line 2x - 3y = 2 and its co-ordinates on that line are (4, 2). Now, at another instant, the same particle is moving along a straight line 3x + 4y = 7 and its co-ordinates are (1, 1). Find the co-ordinates of that axis about which it is in pure rotation.a)30/17 , 35/17b)50/17 , 61/17c)8/9 , 16/9d)None of theseCorrect answer is option 'B'. Can you explain this answer? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE 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