Young-Laplace law states that the excess pressure inside a soap bubble of radius R is given by `DeltaP = 4 sigma //R` where `sigma` is the coefficient of surface tension of the soap. The `Eoverset(* *)(o) tv overset(* *)(o)s` number `E_0` is a dimensionless number that is used to describe the shape of bubbles rising through a surrounding fluid. It is a combination of g, the acceleration due to gravity, `rho`, the density of the surrounding fluid, `sigma` and a characterstic length scale L which could be the radius of the bubble. A possible expression for `E_0` is

Options

A. `(rhog)/(sigmaL^3)`
B. `(rhoL^2)/(sigmag)`
C. `(rhogL^2)/(sigma)`
D. `(gL^2)/(sigma rho)`

Answer

C

Explanation

Check dimensionally
as `sigma=F/l implies [sigma]=([MLT^(-2)])/([L])`
`implies [sigma] =[MT^(-2)]`
`g = [LT^(-2)]`
and `rho = [ML^(-3)]`
Now, `(rhogL^2)/(sigma)=([ML^(-3)][LT^(-2)][L^2])/([MT^(-2)])`
`= [M^(0)L^(0)T^(0)]`