First slide

Dimensions of physical quantities

Question

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

Moderate

A

x and B
B

C and z^-1
C

y and B/A
D

x and A

Solution

$\begin{array}{l} [x] = [A y] = [B] \\ \Rightarrow [y] = [B / A] \\ a n d [x] = [B] \\ Also, [x] \neq [A] and [C z] = dimensionless \\ \Rightarrow [C] = [z^{- 1}] \end{array}$

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