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In dimension of critical velocity v(c) l...

In dimension of critical velocity `v_(c)` 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

A

1,1,1

B

1,-1,-1

C

`-1,-1,1`

D

`-1,-1,-1`

Text Solution

Verified by Experts

The correct Answer is:
B
`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
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