Question

Given $x=Ay+B \tan\left(C z\right)$ , where $x,y,z$ are physical quantities while $A,B,C$ are constants. Then ___ and ___ do not have the same dimensions. Fill in the blanks.

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

Answer 1

Answer: (D)

Given that
$x=Ay+B \tan\left(C z\right)$
From the homogeneity principle,
$\left[x\right]=\left[Ay\right]=\left[B\right]\Rightarrow \left[\frac{x}{A}\right]=\left[y\right]=\left[\frac{B}{A}\right]$
$\left[C z\right]=M^{0}L^{0}T^{0}$
because trigonometric functions doesn't have dimensions.
$x$ and $B;$ $C$ and $Z^{- 1};$ $y$ and $\frac{B}{A}$ have the same dimension but $x$ and $A$ have the different dimensions.