Question

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

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

Answer 1

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

Given $x=Ay+Btan\left(C_z\right)$

Each term in a equation has same dimensions.

$\Rightarrow Dim\left(x\right)=Dim\left(Ay\right)=Dim\left(B\right)$

$\Rightarrow$ $x$ and $A$ cannot have same dimension.