Question

A physical quantity $x$ depends on quantities $y$ and $z$ as follows: $x=Ay+B\tan \left(Cz\right)$, 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 $B/A$
• D. $x$ and $A$

Answer 1

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

From the given equation, using principle of homogeneity:
$\left[x\right]=\left[A\right]\left[y\right]=\left[B\right]$
and $\left[C\right]\left[z\right]=1$

So, we can say that $\left[x\right]=\left[B\right]$, $\left[C\right]=\left[z^{-1}\right]$ and $\left[y\right]=\frac{\left[B\right]}{\left[A\right]}$.