In dimension of circal velocity `v_(0)` liquid following through a take are expressed as `(eta^(x) rho^(y) r^(z))` where `eta, rhoand r `are the coefficient of viscosity of liquid density of liquid and radius of the tube respectively then the value of `x,y` and `z` are given by

Options

A. `1,1,1`
B. `1,-1,-1`
C. `-1,-1,1`
D. `-1,-1,-1`

Answer

b

Explanation

`v_(c) = [eta^(x) rho^(y)r^(z)]`
`[L^(1)T^(-1)] = [M^(1)L^(-1) T^(-1)]^(x) [M^(1)L^(-3)]^(y) [L^(1)]^(z)`
`[L^(1)T^(-1)] prop [M^(x+y)] [L^(-x +3y +z)] [T^(-x)]`
taking comparison an both sides
`x + y = 0 , -x - 3y + z= 1 , -x = -1`
`rArr x=1 , y= -1 , z= -1`