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`
From the dimensional homogenetly
`[x] - [Ay] = [B] rArr ([x)/(A]) = [y] = ([B)/(A))]`
`[cz] = [M^(0) L^(0)T^(0)] =` Dimension less
`x` and `A` have the different dimensionsx and `B, C` and `z^(-1), y` and `(B)/(A)` have the same dimension but `x` amd `A` have the different dimensions.