Mechanical Engineering Exam > Mechanical Engineering Questions > According to Lami’s theorem, if three c...
Start Learning for Free
According to Lami’s theorem, if three coplanar forces are acting at a point b in equilibrium, then each force is proportional to the ______ of the angle between the other two.
- a)sine
- b)tangent
- c)sec
- d)cosine
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
According to Lami’s theorem, if three coplanar forces are acting...
Understanding Lami's Theorem
Lami's theorem is a fundamental principle in mechanical engineering that deals with the equilibrium of forces acting at a point. It applies specifically to three coplanar forces and provides a method to understand the relationship between these forces.
Key Concepts of Lami's Theorem
- Lami's theorem states that if three coplanar forces \( F_1, F_2, \) and \( F_3 \) are acting at a point and are in equilibrium, then:
\[
\frac{F_1}{\sin A} = \frac{F_2}{\sin B} = \frac{F_3}{\sin C}
\]
where \( A, B, \) and \( C \) are the angles opposite to the respective forces.
Proportionality to Sine of Angles
- The theorem highlights that each force is proportional to the sine of the angle opposite to it. Thus, if you know the magnitudes of two forces and the angle between them, you can find the third force.
Why Sine?
- The sine function relates to the geometry of triangles formed by the forces. In a triangle, the length of a side (representing the force) is proportionate to the sine of the angle opposite to that side. This relationship remains true for equilibrium scenarios, ensuring that the forces balance each other.
Conclusion
- Hence, according to Lami's theorem, each force acting at point B in equilibrium is proportional to the **sine** of the angle between the other two forces. This principle is essential for analyzing static equilibrium in mechanical systems, making option 'A' the correct answer.
Lami's theorem is a fundamental principle in mechanical engineering that deals with the equilibrium of forces acting at a point. It applies specifically to three coplanar forces and provides a method to understand the relationship between these forces.
Key Concepts of Lami's Theorem
- Lami's theorem states that if three coplanar forces \( F_1, F_2, \) and \( F_3 \) are acting at a point and are in equilibrium, then:
\[
\frac{F_1}{\sin A} = \frac{F_2}{\sin B} = \frac{F_3}{\sin C}
\]
where \( A, B, \) and \( C \) are the angles opposite to the respective forces.
Proportionality to Sine of Angles
- The theorem highlights that each force is proportional to the sine of the angle opposite to it. Thus, if you know the magnitudes of two forces and the angle between them, you can find the third force.
Why Sine?
- The sine function relates to the geometry of triangles formed by the forces. In a triangle, the length of a side (representing the force) is proportionate to the sine of the angle opposite to that side. This relationship remains true for equilibrium scenarios, ensuring that the forces balance each other.
Conclusion
- Hence, according to Lami's theorem, each force acting at point B in equilibrium is proportional to the **sine** of the angle between the other two forces. This principle is essential for analyzing static equilibrium in mechanical systems, making option 'A' the correct answer.
Free Test
FREE
| Start Free Test |
Community Answer
According to Lami’s theorem, if three coplanar forces are acting...
Lami's theorem:
It states that if three forces acting at a point are in equilibrium, each force is proportional to the sine of the angle between the other two forces.
Consider three forces FA, FB, FC acting on a particle or rigid body making angles α, β and γ with each other.
Then from Lami's theorem,
It states that if three forces acting at a point are in equilibrium, each force is proportional to the sine of the angle between the other two forces.
Consider three forces FA, FB, FC acting on a particle or rigid body making angles α, β and γ with each other.
Then from Lami's theorem,
Attention Mechanical Engineering Students!
To make sure you are not studying endlessly, EduRev has designed Mechanical Engineering study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Mechanical Engineering.
|
Explore Courses for Mechanical Engineering exam
|
|
Similar Mechanical Engineering Doubts
Top Courses for Mechanical EngineeringView all
According to Lami’s theorem, if three coplanar forces are acting at a point b in equilibrium, then each force is proportional to the ______ of the angle between the other two.a)sineb)tangentc)secd)cosineCorrect answer is option 'A'. Can you explain this answer?
Question Description
According to Lami’s theorem, if three coplanar forces are acting at a point b in equilibrium, then each force is proportional to the ______ of the angle between the other two.a)sineb)tangentc)secd)cosineCorrect answer is option 'A'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about According to Lami’s theorem, if three coplanar forces are acting at a point b in equilibrium, then each force is proportional to the ______ of the angle between the other two.a)sineb)tangentc)secd)cosineCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for According to Lami’s theorem, if three coplanar forces are acting at a point b in equilibrium, then each force is proportional to the ______ of the angle between the other two.a)sineb)tangentc)secd)cosineCorrect answer is option 'A'. Can you explain this answer?.
According to Lami’s theorem, if three coplanar forces are acting at a point b in equilibrium, then each force is proportional to the ______ of the angle between the other two.a)sineb)tangentc)secd)cosineCorrect answer is option 'A'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about According to Lami’s theorem, if three coplanar forces are acting at a point b in equilibrium, then each force is proportional to the ______ of the angle between the other two.a)sineb)tangentc)secd)cosineCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for According to Lami’s theorem, if three coplanar forces are acting at a point b in equilibrium, then each force is proportional to the ______ of the angle between the other two.a)sineb)tangentc)secd)cosineCorrect answer is option 'A'. Can you explain this answer?.
Solutions for According to Lami’s theorem, if three coplanar forces are acting at a point b in equilibrium, then each force is proportional to the ______ of the angle between the other two.a)sineb)tangentc)secd)cosineCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Mechanical Engineering.
Download more important topics, notes, lectures and mock test series for Mechanical Engineering Exam by signing up for free.
Here you can find the meaning of According to Lami’s theorem, if three coplanar forces are acting at a point b in equilibrium, then each force is proportional to the ______ of the angle between the other two.a)sineb)tangentc)secd)cosineCorrect answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
According to Lami’s theorem, if three coplanar forces are acting at a point b in equilibrium, then each force is proportional to the ______ of the angle between the other two.a)sineb)tangentc)secd)cosineCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for According to Lami’s theorem, if three coplanar forces are acting at a point b in equilibrium, then each force is proportional to the ______ of the angle between the other two.a)sineb)tangentc)secd)cosineCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of According to Lami’s theorem, if three coplanar forces are acting at a point b in equilibrium, then each force is proportional to the ______ of the angle between the other two.a)sineb)tangentc)secd)cosineCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice According to Lami’s theorem, if three coplanar forces are acting at a point b in equilibrium, then each force is proportional to the ______ of the angle between the other two.a)sineb)tangentc)secd)cosineCorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice Mechanical Engineering tests.
|
|
Explore Courses for Mechanical Engineering 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
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup