Young-Laplace law states that the excess pressure inside a soap bubble of radius $R$ is given by $\Delta P = 4 \sigma / R$,where $\sigma$ 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 $g$ (acceleration due to gravity),$\rho$ (density of the surrounding fluid),$\sigma$ (surface tension),and a characteristic length scale $L$ (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
    $\frac{\rho g L^2}{\sigma}$
  • D
    $\frac{g L^2}{\sigma \rho}$

Explore More

Similar Questions

If speed of light in vacuum $\left(3 \times 10^8 \,m/s\right)$, acceleration due to gravity $\left(10 \,m/s^2\right)$ and mass of electron $\left(9.1 \times 10^{-31} \,kg\right)$ are taken as fundamental physical quantities, then the unit of time in this system is

$A$ new system of units is proposed in which the unit of mass is $\alpha \ kg$,the unit of length is $\beta \ m$,and the unit of time is $\gamma \ s$. How much will $5 \ J$ measure in this new system?

Difficult
View Solution

Which of the following expressions can be deduced on the basis of dimensional analysis? (All symbols have their usual meanings)

Given below are two statements: One is labelled as Assertion $(A)$ and other is labelled as Reason $(R)$.
Assertion $(A)$: Time period of oscillation of a liquid drop depends on surface tension $(S)$,if density of the liquid is $\rho$ and radius of the drop is $r$,then $T = k \sqrt{\rho r^{3} / S}$ is dimensionally correct,where $k$ is dimensionless.
Reason $(R)$: Using dimensional analysis,we find that the $R.H.S.$ has different dimensions than that of the time period.

If the force is given by $F = at + bt^2$ where $t$ is time,the dimensions of $a$ and $b$ are:

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo