Sol:

\( [v] = [LT^{-1}] \) \( \eta = \frac{F}{A\frac{dv}{dx}} \) \( \Rightarrow [\eta] = \frac{[MLT^{-2}]}{[L^{2}][T^{-1}]} \) \( \Rightarrow [M^{1}L^{-1}T^{1}] \) \( [\rho ] = [ML^{-3}] \) \( \Rightarrow [LT^{-1}] = [M^{1}L^{-1}T^{-1}]^{x} [ML^{-3}]^{y} [L]^{z} \)

Now by equating the exponents of M, L and T on both LHS and RHS, we get 

\( \Rightarrow M^{0} = M^{(x+y)} \) \( \Rightarrow y = – x \)

For T 

 = -1 = -x

x= 1 

y = -x = -1 

For L

1 = -x – 3y + z

1 = -1 + 3 + z

 1 = 2 + z 

\( \Rightarrow z = -1 \)

Therefore, the values of x, y and z are

x = 1, y = -1 and z = -1

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