Question

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

Answer 1

Correct Answer - d
`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 `B,C` and `Z^(-1), y` and `(B)/(A)` have the different dimensionsx but x and A have the different dimensions