Question

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 have different 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

x=Ay + B tan Cz
From the dimensional homogenity
[x] = [Ay] =[B] $\Rightarrow \left[\frac{x}{A}\right]=\left[y\right]=\left[\frac{B}{A}\right]$
[Cz] = $\left[M^0{L}^0{T}^0\right]=$ 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.