Question

An air bubble of negligible weight having radius r rises steadily through a solution of density σ at speed v. The coefficient of viscosity of the solution is given by ______.

Options

• `eta = (4rsigmag)/(9ν)`

• `eta = (4r^2sigmag)/(9ν)`

• `eta = (2pir^2sigmag)/(9ν)`

• `eta = (2r^2sigmag)/(3piν)`

Answer 1

An air bubble of negligible weight having radius r rises steadily through a solution of density σ at speed v. The coefficient of viscosity of the solution is given by `underlinebb(eta = (2pir^2sigmag)/(9ν))`.

Explanation:

We know that for air bubbles in the liquid.

`ν_T = ν = (2r^2g)/(9eta)(rho_f - rho)`

⇒ `eta = (2r^2g)/(9ν)(rho_f - rho)`

⇒ `eta = (2r^2g)/(9ν)(sigma)` [∵ ρ_f = σ and ρ ≈ ο]