Question

A physical quantity $x$ depends on quantities $y$ and $z$ as follows: $x=Ay+B\tan Cz$, where $A,B$ and $C$ are constants. Which of the following do not have the same dimensions.

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

Answer 1

The correct option is D $x$ and $A$

Given relation is $x=Ay+B\tan Cz$
$\Rightarrow \left[x\right]=\left[A\right]\left[y\right]=\left[B\right]$
$\Rightarrow \left[x\right]\ne \left[A\right]$
Also, $\Rightarrow \left[y\right]=\left[\frac{B}{A}\right]$
and, the dimension of $C$ will be the dimension of $z^{-1}$.