Question

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

• A. $x$ and $B$
• B. $C$ and $z^{-1}$
• C. $y$ and $B/A$
• D. $x$ and $A$

Answer 1

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,
$x=Ay+B\tan \left(Cz\right)$
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 $z^{-1}$ is the same.
Now, the dimension of $Ay$ and $B\tan \left(Cz\right)$ 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 $\left(d\right)$.