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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?
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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.”
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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.
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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?
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