A physcial 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 physcial 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
$x$ and $B$
$C$ and ${z^{ - 1}}$
$y$ and $B/A$
$x$ and $A$
A physcial 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
$x = Ay + B\,\tan Cz$
From the dimensional homogenity
$[x] = [Ay] = [B] \Rightarrow \left[ {\frac{x}{A}} \right] = [y] = \left[ {\frac{B}{A}} \right]$
$[Cz] = [{M^0}{L^0}{T^0}] = $Dimension less
$x$ and $B$; $C$ and ${Z^{ - 1}};y$ and $\frac{B}{A}$ have the same dimension but $x$ and $A$ have the different dimensions.