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

Given that
`x=Ay+Btan(Cz)`
From the homogeneity principle
`[x]=[Ay]=[B]implies[x/A]=[y]`
`=[B/A]`
`Cz=[M^(0)L^(0)T^(0)]`
because trigonometric functions doesn.t have dimensions
x and B, C and `Z^(-1)` y and `B/A` have the same dimension but x and A have the different dimensions.