Question

Young-Laplace law states that the excess pressure inside a soap bubble of radius $R$ is given by $AP = 4\sigma / R,$ where a is the coefficient of surface tension of the soap. The $EOTVOS$ 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 surround in $g$ fluid $\rho$ and a characteristic length scale $L_4$ which could be the radius of the bubble. A possible expression for $E_0$ is

• A. $\frac{\rho g}{\sigma L^{3}}$
• B. $\frac{\rho L^{2}}{\sigma g}$
• C. $\frac{\rho gL^{2}}{\sigma}$
• D. $\frac{gL^{2}}{\sigma\rho}$

Answer 1

Answer: (C)

As $EOTVOS$ number $E_{0}$ is dimensionless, we check dimensions of options given to the choose correct answer.
Now $\left[\frac{\rho gL^{2}}{\sigma}\right]=\frac{\left[\rho\right].\left[g\right].\left[L\right]^{2}}{\left[\sigma\right]}$
$=\frac{\left[ML^{-3}\right]\left[LT^{-2}\right].\left[L\right]^{2}}{\left[ML^{-2}\right]}$
$=\left[m^{0}L^{0}T^{0}\right]=$ Dimensionless