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

Options

A. x and B
B. `C and z^(-1)`
C. y and B / A
D. x and A

Answer

D

Explanation

x = Ay + B tan Cz
[x] = [Ay] = [B] `implies [x/A] =[y] =[B/A]`
[Cz] = `[M^0L^0 T^0]` = Dimensionless
x and B , C and `z^(-1) , y and B/A` have the same dimension but x and A have different dimension.