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)`
`M^(0)L^(1)T^(-1)=(M^(1)L^(-1)T^(-1))^(x)(M^(1)L^(-3))^(y)(L^(1))^(z)`
`M^(0)L^(1)T^(-1)=M^(x+y)L^(-3-3y+z)T^(-x)`
`-x=-1`
x=1 . . . (1)
x+y=0=0
y=-x=-1 . . . (2)
`-x-3y+z=1`
`-1-3(-1)+z=1`
z=-1