Class 11 Exam > Class 11 Questions > If an equation is dimensionally consistenta)d...
Start Learning for Free
If an equation is dimensionally consistent
- a)dimensions of the left hand side and right hand side of the equation are the same
- b)dimensions of the left hand side and right hand side of the equation differ by 1
- c)dimensions of the left hand side and right hand side of the equation differ by 2
- d)dimensions of the left hand side and right hand side of the equation are different
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
If an equation is dimensionally consistenta)dimensions of the left han...
Principle of homogenity of dimensions states that “For an equation to be dimansionally correct, the dimensions of each term on LHS must be equal to the dimensions of each term on RHS.”
Most Upvoted Answer
If an equation is dimensionally consistenta)dimensions of the left han...
**A) Dimensions of the left hand side and right hand side of the equation are the same.**
In physics, dimensions are used to describe the nature of physical quantities. They represent the fundamental properties of a physical quantity, such as length, time, mass, etc. Each physical quantity can be expressed in terms of a combination of these fundamental dimensions.
When we say that an equation is dimensionally consistent, it means that the dimensions on both sides of the equation are the same. In other words, the physical quantities involved in the equation have the same dimensions.
To understand this concept better, let's consider an example:
Suppose we have an equation that describes the distance traveled by an object undergoing constant acceleration:
\[s = ut + \frac{1}{2}at^2\]
Here, 's' represents distance, 'u' represents initial velocity, 't' represents time, and 'a' represents acceleration. Let's analyze the dimensions of each term in the equation:
- The dimension of 's' is length (L).
- The dimension of 'u' is velocity (LT^-1).
- The dimension of 't' is time (T).
- The dimension of 'a' is acceleration (LT^-2).
Now, let's calculate the dimensions of each term on both sides of the equation:
- The dimension of 'ut' is (LT^-1)(T) = L.
- The dimension of \(\frac{1}{2}at^2\) is \(\frac{1}{2}(LT^-2)(T^2) = L\).
As we can see, the dimensions of both terms on the right-hand side of the equation are the same as the dimension of 's' on the left-hand side. Therefore, the equation is dimensionally consistent.
By checking the dimensions of each term in an equation, we can verify its correctness and ensure that the equation represents a valid relationship between physical quantities. If the dimensions on both sides of the equation are not the same, it indicates an error in the equation or a mismatch in the dimensions of the quantities involved.
Hence, the correct answer is option A: Dimensions of the left hand side and right hand side of the equation are the same.
In physics, dimensions are used to describe the nature of physical quantities. They represent the fundamental properties of a physical quantity, such as length, time, mass, etc. Each physical quantity can be expressed in terms of a combination of these fundamental dimensions.
When we say that an equation is dimensionally consistent, it means that the dimensions on both sides of the equation are the same. In other words, the physical quantities involved in the equation have the same dimensions.
To understand this concept better, let's consider an example:
Suppose we have an equation that describes the distance traveled by an object undergoing constant acceleration:
\[s = ut + \frac{1}{2}at^2\]
Here, 's' represents distance, 'u' represents initial velocity, 't' represents time, and 'a' represents acceleration. Let's analyze the dimensions of each term in the equation:
- The dimension of 's' is length (L).
- The dimension of 'u' is velocity (LT^-1).
- The dimension of 't' is time (T).
- The dimension of 'a' is acceleration (LT^-2).
Now, let's calculate the dimensions of each term on both sides of the equation:
- The dimension of 'ut' is (LT^-1)(T) = L.
- The dimension of \(\frac{1}{2}at^2\) is \(\frac{1}{2}(LT^-2)(T^2) = L\).
As we can see, the dimensions of both terms on the right-hand side of the equation are the same as the dimension of 's' on the left-hand side. Therefore, the equation is dimensionally consistent.
By checking the dimensions of each term in an equation, we can verify its correctness and ensure that the equation represents a valid relationship between physical quantities. If the dimensions on both sides of the equation are not the same, it indicates an error in the equation or a mismatch in the dimensions of the quantities involved.
Hence, the correct answer is option A: Dimensions of the left hand side and right hand side of the equation are the same.
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
|
|
Top Courses for Class 11View all
If an equation is dimensionally consistenta)dimensions of the left hand side and right hand side of the equation are the sameb)dimensions of the left hand side and right hand side of the equation differ by 1c)dimensions of the left hand side and right hand side of the equation differ by 2d)dimensions of the left hand side and right hand side of the equation are differentCorrect answer is option 'A'. Can you explain this answer?
Question Description
If an equation is dimensionally consistenta)dimensions of the left hand side and right hand side of the equation are the sameb)dimensions of the left hand side and right hand side of the equation differ by 1c)dimensions of the left hand side and right hand side of the equation differ by 2d)dimensions of the left hand side and right hand side of the equation are differentCorrect answer is option 'A'. 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 If an equation is dimensionally consistenta)dimensions of the left hand side and right hand side of the equation are the sameb)dimensions of the left hand side and right hand side of the equation differ by 1c)dimensions of the left hand side and right hand side of the equation differ by 2d)dimensions of the left hand side and right hand side of the equation are differentCorrect answer is option 'A'. 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 If an equation is dimensionally consistenta)dimensions of the left hand side and right hand side of the equation are the sameb)dimensions of the left hand side and right hand side of the equation differ by 1c)dimensions of the left hand side and right hand side of the equation differ by 2d)dimensions of the left hand side and right hand side of the equation are differentCorrect answer is option 'A'. Can you explain this answer?.
If an equation is dimensionally consistenta)dimensions of the left hand side and right hand side of the equation are the sameb)dimensions of the left hand side and right hand side of the equation differ by 1c)dimensions of the left hand side and right hand side of the equation differ by 2d)dimensions of the left hand side and right hand side of the equation are differentCorrect answer is option 'A'. 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 If an equation is dimensionally consistenta)dimensions of the left hand side and right hand side of the equation are the sameb)dimensions of the left hand side and right hand side of the equation differ by 1c)dimensions of the left hand side and right hand side of the equation differ by 2d)dimensions of the left hand side and right hand side of the equation are differentCorrect answer is option 'A'. 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 If an equation is dimensionally consistenta)dimensions of the left hand side and right hand side of the equation are the sameb)dimensions of the left hand side and right hand side of the equation differ by 1c)dimensions of the left hand side and right hand side of the equation differ by 2d)dimensions of the left hand side and right hand side of the equation are differentCorrect answer is option 'A'. Can you explain this answer?.
Solutions for If an equation is dimensionally consistenta)dimensions of the left hand side and right hand side of the equation are the sameb)dimensions of the left hand side and right hand side of the equation differ by 1c)dimensions of the left hand side and right hand side of the equation differ by 2d)dimensions of the left hand side and right hand side of the equation are differentCorrect answer is option 'A'. 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 If an equation is dimensionally consistenta)dimensions of the left hand side and right hand side of the equation are the sameb)dimensions of the left hand side and right hand side of the equation differ by 1c)dimensions of the left hand side and right hand side of the equation differ by 2d)dimensions of the left hand side and right hand side of the equation are differentCorrect answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
If an equation is dimensionally consistenta)dimensions of the left hand side and right hand side of the equation are the sameb)dimensions of the left hand side and right hand side of the equation differ by 1c)dimensions of the left hand side and right hand side of the equation differ by 2d)dimensions of the left hand side and right hand side of the equation are differentCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for If an equation is dimensionally consistenta)dimensions of the left hand side and right hand side of the equation are the sameb)dimensions of the left hand side and right hand side of the equation differ by 1c)dimensions of the left hand side and right hand side of the equation differ by 2d)dimensions of the left hand side and right hand side of the equation are differentCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of If an equation is dimensionally consistenta)dimensions of the left hand side and right hand side of the equation are the sameb)dimensions of the left hand side and right hand side of the equation differ by 1c)dimensions of the left hand side and right hand side of the equation differ by 2d)dimensions of the left hand side and right hand side of the equation are differentCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice If an equation is dimensionally consistenta)dimensions of the left hand side and right hand side of the equation are the sameb)dimensions of the left hand side and right hand side of the equation differ by 1c)dimensions of the left hand side and right hand side of the equation differ by 2d)dimensions of the left hand side and right hand side of the equation are differentCorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice Class 11 tests.
|
|
Explore Courses for Class 11 exam
|
|
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