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A physical quantity x depends on quantities y and z as x = Ay B sin (C z), where A, B, and C are constants. Which of the following have same dimensions? (1) x and Ay (2) x and B (3) C and z-1 (4) All of the above?
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A physical quantity x depends on quantities y and z as x = Ay B sin ...
Dimensions of Physical Quantities in Equations
X = AY B sin (CZ)
In this equation, physical quantity X depends on physical quantities Y and Z. A, B, and C are constants.
Dimensions of X and AY
X has the dimensions of Y multiplied by the dimensions of B sin (CZ). Therefore, X and AY have the same dimensions, as A is a constant and does not affect the dimensions of Y.
Dimensions of X and B
B is a constant and does not depend on any other physical quantity, so its dimensions are simply the dimensions of X.
Dimensions of C and Z-1
The sin function is dimensionless, so the dimensions of B and X are determined by the dimensions of sin (CZ). Therefore, C must have dimensions of Z-1 in order for the argument of the sin function to be dimensionless.
Conclusion
Therefore, the answer is (4) All of the above. X and AY have the same dimensions because A is a constant. X and B have the same dimensions because B is a constant. C and Z-1 have the same dimensions because the sin function is dimensionless.
X = AY B sin (CZ)
In this equation, physical quantity X depends on physical quantities Y and Z. A, B, and C are constants.
Dimensions of X and AY
X has the dimensions of Y multiplied by the dimensions of B sin (CZ). Therefore, X and AY have the same dimensions, as A is a constant and does not affect the dimensions of Y.
Dimensions of X and B
B is a constant and does not depend on any other physical quantity, so its dimensions are simply the dimensions of X.
Dimensions of C and Z-1
The sin function is dimensionless, so the dimensions of B and X are determined by the dimensions of sin (CZ). Therefore, C must have dimensions of Z-1 in order for the argument of the sin function to be dimensionless.
Conclusion
Therefore, the answer is (4) All of the above. X and AY have the same dimensions because A is a constant. X and B have the same dimensions because B is a constant. C and Z-1 have the same dimensions because the sin function is dimensionless.
Community Answer
A physical quantity x depends on quantities y and z as x = Ay B sin ...
The first answer is correct because in the form of sin it is difference
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A physical quantity x depends on quantities y and z as x = Ay B sin (C z), where A, B, and C are constants. Which of the following have same dimensions? (1) x and Ay (2) x and B (3) C and z-1 (4) All of the above?
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A physical quantity x depends on quantities y and z as x = Ay B sin (C z), where A, B, and C are constants. Which of the following have same dimensions? (1) x and Ay (2) x and B (3) C and z-1 (4) All of the above? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A physical quantity x depends on quantities y and z as x = Ay B sin (C z), where A, B, and C are constants. Which of the following have same dimensions? (1) x and Ay (2) x and B (3) C and z-1 (4) All of the above? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A physical quantity x depends on quantities y and z as x = Ay B sin (C z), where A, B, and C are constants. Which of the following have same dimensions? (1) x and Ay (2) x and B (3) C and z-1 (4) All of the above?.
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