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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 prop [ eta ^(x) rho ^(y) r^(z)]`
`[L^(1)T^(-1)] prop [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 comparision on both size
` x+y =0, -x - 3y +z =1, -x =-1`
`rArr x =1, y =-1, z=-1`
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