In dimension of critical velocity `v_(c)` of liquid following through a tube are expressed as `[eta^(x)rho^(y)r^(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

Options

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

Explanation

`v_(c) prop eta^(x) rho^(y) r^(z)`
`:.v_(c)=k eta^(x) rho^(y) r^(z)` Where k is dimensionless Writtingh dimension formula on both the side,
`M^(0)L^(1)T^(-1)=(M^(1)L^(-1)T^(-1))^(x) xx (M^(1)L^(-3)T^(0))xx (M^(0)L^(1)T^(0))^(z)`
`:. M^(0)L^(1)T^(-1)=M^(x)L^(-x)xx M^(y)L^(-3)T^(0)xx L^(z)`
`=M^(x+y)L^(-x-3y+z)T^(-x)`
Comparing powerof M,L,T
`0=x+y " " 1=-x-3y+z " " -1=-x`
`:.1=-1-3(-1)+z :. x=1`
`:. 0=1+y " " :.1=-1+3+z`
`:.y=-1" " :. -1=z`
`:.x=1, y=-1 , z=-1`