If dimension of critical velocity $v_{c}$ , of liquid flowing through a tube is expressed as $(η^{x} ρ^{y} r^{z})$ , where $η, ρ$ and $r$ 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 :

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$- 1, - 1, 1$

$1, 1, 1$

$- 1, - 1, - 1$

$1, - 1, - 1$

answer is B.

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Detailed Solution

$v_{c} \propto [η^{x} ρ^{y} r^{z}] [L^{1} T^{1}] \propto {[M^{1} L^{- 1} T^{- 1}]}^{x} [M^{1} L^{- 3}]^{y} {[L^{1}]}^{z} [L^{1} T^{- 1}] \propto [M^{x + y}] [L^{- x - 3 y + z}] [T^{- x}]$

taking comparison on both size

$x + y = 0, - x - 3 y + z = 1, - x = - 1 \Rightarrow x = 1, y = - 1, z = - 1$

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