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Q.

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

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a

–1, –1, 1

b

1, –1,–1

c

1, 1, 1

d

–1, –1, –1

answer is B.

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Detailed Solution

$v_{c} \propto [η^{x} ρ^{y} r^{z}] [L^{1} T^{- 1}] \propto {[M^{1} L^{- 1} T^{- 1}]}^{x} {[M^{1} L^{- 3}]}^{y} {[L^{1}]}^{z} [L^{1} T^{- 1}] \propto [M^{x + y}] [L^{- x - 3 y + z}] [T^{- x}] T a k i n g c o m p a r i s o n o n b o t h s i d e s, x + y = 0, - x - 3 y + z = 1, - x = - 1 \Rightarrow x = 1, y = - 1, z = - 1$

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In dimension of critical velocity vc of liquid flowing through a tube are expressed as ηx,ρy,rz where η,ρ 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: