A physical quantity \(x\) depends on quantities \(y\) and \(z\) as follows: \(x=A y+B \tan (C z)\), where…

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 constants. Which of the following do not have the same dimensions?
  1. \(x\) and \(B\)
  2. \(C\) and \(z^{-1}\)
  3. \(y\) and \(B / A\)
  4. \(x\) and \(A\)

Solution

\([x]=[A y]=[B] \Rightarrow[y]=[B / A]\)
Also, \([x] \neq[A]\) and \([C z]=\) dimensionless
\(\Rightarrow[C]=\left[z^{-1}\right]\)

Asked in: JEE Mains - Units and Dimensions - Chapter Test

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