Class 11 Exam > Class 11 Questions > Two forces are such that the sum of their mag...
Start Learning for Free
Two forces are such that the sum of their magnitudes is 18 N and their resultant which has magnitude 12 N, is perpendicular to the smaller force. Then the magnitudes of the forces are
- a)12 N, 6 N
- b)13 N, 5 N
- c)10 N, 8 N
- d)16 N, 2 N
Correct answer is option 'B'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
Two forces are such that the sum of their magnitudes is 18 N and their...
Solving Eqs. (i), (ii) and (iii), A = 5N, B = 13N
Most Upvoted Answer
Two forces are such that the sum of their magnitudes is 18 N and their...
Free Test
FREE
| Start Free Test |
Community Answer
Two forces are such that the sum of their magnitudes is 18 N and their...
Given information:
- The sum of the magnitudes of two forces is 18 N.
- The resultant force has a magnitude of 12 N.
- The resultant force is perpendicular to the smaller force.
Let's assume the magnitudes of the two forces are F1 and F2, with F1 being the smaller force. According to the given information, we can write the following equations:
Equation 1: F1 + F2 = 18 N
Equation 2: √(F1^2 + F2^2) = 12 N
To find the magnitudes of the forces, we can solve these two equations simultaneously.
Solving the equations:
From Equation 2, we can square both sides to eliminate the square root:
F1^2 + F2^2 = 144
Now, let's square Equation 1:
(F1 + F2)^2 = (18 N)^2
F1^2 + 2F1F2 + F2^2 = 324
Substituting the value of F1^2 + F2^2 from the previous equation into this equation:
144 + 2F1F2 = 324
2F1F2 = 324 - 144
2F1F2 = 180
F1F2 = 90
Since the resultant force is perpendicular to the smaller force, we can use the concept of vectors to determine that the dot product of the two forces is zero:
F1 * F2 * cosθ = 0
Since cosθ = 0 (angle between the forces is 90 degrees), we have:
F1 * F2 = 0
Substituting the value of F1F2 = 90 into this equation, we get:
90 = 0
This is not a valid equation, so our assumption that cosθ = 0 is incorrect. Therefore, cosθ ≠ 0, which implies that the angle between the forces is not 90 degrees.
Conclusion:
Based on the given information, it is not possible to determine the magnitudes of the forces. Therefore, none of the given options (A, B, C, D) are correct.
- The sum of the magnitudes of two forces is 18 N.
- The resultant force has a magnitude of 12 N.
- The resultant force is perpendicular to the smaller force.
Let's assume the magnitudes of the two forces are F1 and F2, with F1 being the smaller force. According to the given information, we can write the following equations:
Equation 1: F1 + F2 = 18 N
Equation 2: √(F1^2 + F2^2) = 12 N
To find the magnitudes of the forces, we can solve these two equations simultaneously.
Solving the equations:
From Equation 2, we can square both sides to eliminate the square root:
F1^2 + F2^2 = 144
Now, let's square Equation 1:
(F1 + F2)^2 = (18 N)^2
F1^2 + 2F1F2 + F2^2 = 324
Substituting the value of F1^2 + F2^2 from the previous equation into this equation:
144 + 2F1F2 = 324
2F1F2 = 324 - 144
2F1F2 = 180
F1F2 = 90
Since the resultant force is perpendicular to the smaller force, we can use the concept of vectors to determine that the dot product of the two forces is zero:
F1 * F2 * cosθ = 0
Since cosθ = 0 (angle between the forces is 90 degrees), we have:
F1 * F2 = 0
Substituting the value of F1F2 = 90 into this equation, we get:
90 = 0
This is not a valid equation, so our assumption that cosθ = 0 is incorrect. Therefore, cosθ ≠ 0, which implies that the angle between the forces is not 90 degrees.
Conclusion:
Based on the given information, it is not possible to determine the magnitudes of the forces. Therefore, none of the given options (A, B, C, D) are correct.
Attention Class 11 Students!
To make sure you are not studying endlessly, EduRev has designed Class 11 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 11.
|
Explore Courses for Class 11 exam
|
|
Similar Class 11 Doubts
Top Courses for Class 11View all
Two forces are such that the sum of their magnitudes is 18 N and their resultant which has magnitude 12 N, is perpendicular to the smaller force. Then the magnitudes of the forces area)12 N, 6 Nb)13 N, 5 Nc)10 N, 8 Nd)16 N, 2 NCorrect answer is option 'B'. Can you explain this answer?
Question Description
Two forces are such that the sum of their magnitudes is 18 N and their resultant which has magnitude 12 N, is perpendicular to the smaller force. Then the magnitudes of the forces area)12 N, 6 Nb)13 N, 5 Nc)10 N, 8 Nd)16 N, 2 NCorrect answer is option 'B'. Can you explain this answer? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Two forces are such that the sum of their magnitudes is 18 N and their resultant which has magnitude 12 N, is perpendicular to the smaller force. Then the magnitudes of the forces area)12 N, 6 Nb)13 N, 5 Nc)10 N, 8 Nd)16 N, 2 NCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two forces are such that the sum of their magnitudes is 18 N and their resultant which has magnitude 12 N, is perpendicular to the smaller force. Then the magnitudes of the forces area)12 N, 6 Nb)13 N, 5 Nc)10 N, 8 Nd)16 N, 2 NCorrect answer is option 'B'. Can you explain this answer?.
Two forces are such that the sum of their magnitudes is 18 N and their resultant which has magnitude 12 N, is perpendicular to the smaller force. Then the magnitudes of the forces area)12 N, 6 Nb)13 N, 5 Nc)10 N, 8 Nd)16 N, 2 NCorrect answer is option 'B'. Can you explain this answer? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Two forces are such that the sum of their magnitudes is 18 N and their resultant which has magnitude 12 N, is perpendicular to the smaller force. Then the magnitudes of the forces area)12 N, 6 Nb)13 N, 5 Nc)10 N, 8 Nd)16 N, 2 NCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two forces are such that the sum of their magnitudes is 18 N and their resultant which has magnitude 12 N, is perpendicular to the smaller force. Then the magnitudes of the forces area)12 N, 6 Nb)13 N, 5 Nc)10 N, 8 Nd)16 N, 2 NCorrect answer is option 'B'. Can you explain this answer?.
Solutions for Two forces are such that the sum of their magnitudes is 18 N and their resultant which has magnitude 12 N, is perpendicular to the smaller force. Then the magnitudes of the forces area)12 N, 6 Nb)13 N, 5 Nc)10 N, 8 Nd)16 N, 2 NCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 11.
Download more important topics, notes, lectures and mock test series for Class 11 Exam by signing up for free.
Here you can find the meaning of Two forces are such that the sum of their magnitudes is 18 N and their resultant which has magnitude 12 N, is perpendicular to the smaller force. Then the magnitudes of the forces area)12 N, 6 Nb)13 N, 5 Nc)10 N, 8 Nd)16 N, 2 NCorrect answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Two forces are such that the sum of their magnitudes is 18 N and their resultant which has magnitude 12 N, is perpendicular to the smaller force. Then the magnitudes of the forces area)12 N, 6 Nb)13 N, 5 Nc)10 N, 8 Nd)16 N, 2 NCorrect answer is option 'B'. Can you explain this answer?, a detailed solution for Two forces are such that the sum of their magnitudes is 18 N and their resultant which has magnitude 12 N, is perpendicular to the smaller force. Then the magnitudes of the forces area)12 N, 6 Nb)13 N, 5 Nc)10 N, 8 Nd)16 N, 2 NCorrect answer is option 'B'. Can you explain this answer? has been provided alongside types of Two forces are such that the sum of their magnitudes is 18 N and their resultant which has magnitude 12 N, is perpendicular to the smaller force. Then the magnitudes of the forces area)12 N, 6 Nb)13 N, 5 Nc)10 N, 8 Nd)16 N, 2 NCorrect answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Two forces are such that the sum of their magnitudes is 18 N and their resultant which has magnitude 12 N, is perpendicular to the smaller force. Then the magnitudes of the forces area)12 N, 6 Nb)13 N, 5 Nc)10 N, 8 Nd)16 N, 2 NCorrect answer is option 'B'. Can you explain this answer? tests, examples and also practice Class 11 tests.
|
|
Explore Courses for Class 11 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