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If dimensions of critical velocity $v_c$ of liquid flowing through a tube are expressed as $[\eta^x\rho^yr^z]$, where $\eta$, $\rho$ and r are the coefficient of viscosity of liquid, density of liquid and radius of the tube respectively, then the values of x, y and z are given by:
A
1, 1, 1
B
1, −1, −1
C
−1, −1, 1
D
−1, −1, −1
Detailed Solution
$[LT^{-1}] = [ML^{-1}T^{-1}]^x[ML^{-3}]^y[L]^z = [M^{x+y}L^{-x-3y+z}T^{-x}]$
$-x = -1 \Rightarrow x = 1$; $x + y = 0 \Rightarrow y = -1$; $-x - 3y + z = 1 \Rightarrow z = -1$
$-x = -1 \Rightarrow x = 1$; $x + y = 0 \Rightarrow y = -1$; $-x - 3y + z = 1 \Rightarrow z = -1$