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+BtanCz`
From the dimensional gomogeneity
`[x]=[Ay]=[B]implies[(x)/(A)]=[y]=[(B)/(A)]`
`[Cz]=[M^0L^0T^0]=`dimensionless
x and B, C and `Z^-1`, y and `(B)/(A)` have the same dimension by x and A have the different dimensions.