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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?
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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.
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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
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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?
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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?.
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