A physcial quantity X depends on quantities V and 7Z as follows: \(\bar{x} = A y + B \tan C z\) , where A, B and C are constants. Which of the following do not have the same dimensions
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\(x = Ay + B \tan Cz\)
From the dimensional homogenity
\([x] = [Ay] = [B] \Rightarrow \begin{bmatrix} \frac{x}{A} \end{bmatrix} = [y] = \begin{bmatrix} \frac{B}{A} \end{bmatrix}\)
\(\left[\mathrm{Cz}\right] = \left[\mathrm{M}^{0} \mathrm{L}^{0} \mathrm{T}^{0}\right] =\) Dimension less
X and B ; C and \(Z^{-1} \cdot y\) and \(\frac{B}{A}\) have the same dimension but X and \Delta have the different dimensions.
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