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Question

A physical quantity x depends on other physical quantities y and z as x=Ay+Btan(Cz), where A,B and C are constants. Which of the following do not have the same dimension?

A
x and B
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B
C and z1
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C
y and B/A
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D
x and A
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Solution

The correct option is D x and A
We know that physical quantities having the same dimensions are added or subtracted.
Also, physical quantities having the same dimensions are compared.
Given,
x=Ay+Btan(Cz)
We know that trigonometric ratios are dimensionless, therefore, the dimension of x and B is the same.
Angle is dimensionless, therefore, the dimension of C and z1 is the same.
Now, the dimension of Ay and Btan(Cz) should be the same. Therefore, the dimension of y and B/A is the same.
And, the dimension of Ay and x is the same.
Therefore, correct option is (d).

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