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A physical quantity x depends on quantities y and z as follows: x= Ay + BtanCz , where A,B and C are constants . which of the following do not have the same dimensions
Most Upvoted Answer
A physical quantity x depends on quantities y and z as follows: x= Ay ...
Since tan(x) is dimensionless, the dimension of B is same as that of x.
[x] = [B]
[x] = [A] [y]
Assuming that y is not dimensionless, one can easily say,
[A] is not equal to [B]
hope this answers your question
[x] = [B]
[x] = [A] [y]
Assuming that y is not dimensionless, one can easily say,
[A] is not equal to [B]
hope this answers your question
Community Answer
A physical quantity x depends on quantities y and z as follows: x= Ay ...
Analysis of Dimensions
- Given Equation: x = Ay + BtanCz
- Dimensions of Quantities:
- x has dimensions [x]
- y has dimensions [y]
- z has dimensions [z]
- A, B are constants
- C is dimensionless
Determination of Dimensions
- Dimensions of Ay term:
- Dimensions of Ay = [A][y]
- Therefore, dimensions of Ay = [x]
- Dimensions of BtanCz term:
- Dimensions of BtanCz = [B][C][z]
- Since tanCz is dimensionless, dimensions of BtanCz = [B]
- Comparison of Dimensions:
- Dimensions of Ay = [x]
- Dimensions of BtanCz = [B]
- Conclusion:
- The dimensions of Ay and BtanCz are different
- Therefore, Ay and BtanCz do not have the same dimensions in the given equation
Explanation
In the given equation x = Ay + BtanCz, the terms Ay and BtanCz have different dimensions. The term Ay has dimensions of [x] as it is the product of a constant A and quantity y. On the other hand, the term BtanCz has dimensions of [B] as it is the product of constants B and C, and the tangent function of z which is dimensionless.
Since the dimensions of Ay and BtanCz are different, they cannot be added together unless they are converted to the same dimensions. This is important in physics and mathematics to ensure that equations are mathematically and physically consistent.
Therefore, in the given equation, Ay and BtanCz do not have the same dimensions, and this needs to be taken into account when analyzing the physical quantity x.
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A physical quantity x depends on quantities y and z as follows: x= Ay + BtanCz , where A,B and C are constants . which of the following do not have the same dimensions
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A physical quantity x depends on quantities y and z as follows: x= Ay + BtanCz , where A,B and C are constants . which of the following do not have the same dimensions for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A physical quantity x depends on quantities y and z as follows: x= Ay + BtanCz , where A,B and C are constants . which of the following do not have the same dimensions covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A physical quantity x depends on quantities y and z as follows: x= Ay + BtanCz , where A,B and C are constants . which of the following do not have the same dimensions .
A physical quantity x depends on quantities y and z as follows: x= Ay + BtanCz , where A,B and C are constants . which of the following do not have the same dimensions for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A physical quantity x depends on quantities y and z as follows: x= Ay + BtanCz , where A,B and C are constants . which of the following do not have the same dimensions covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A physical quantity x depends on quantities y and z as follows: x= Ay + BtanCz , where A,B and C are constants . which of the following do not have the same dimensions .
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