MCQ
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 $g$, the acceleration due to gravity $\rho$ the density of the surrounding fluid $\sigma$ and a characteristic length scale $L$ which could be the radius of the bubble. A possible expression for $E_0$ is 
  • A
    $\frac{\rho g}{\sigma L^3}$
  • B
    $\frac{\rho L^2}{\sigma g}$
  • $\frac{\rho g L^2}{\sigma}$
  • D
    $\frac{g L^2}{\sigma \rho}$

Answer

Correct option: C.
$\frac{\rho g L^2}{\sigma}$
c
(c)

As EOTVOS number $E_{\text {s }}$ is dimensionless, we check dimensions of options given to the choose correct answer.

Now, $\left[\frac{\rho g I^2}{\sigma}\right]=\frac{[\rho] \cdot[g] \cdot[L]^2}{[\sigma]}$

$=\frac{\left[ ML ^{-3}\right] \cdot\left[ LT ^{-2}\right] \cdot\left[ I ^2\right]}{\left[ MT ^{-2}\right]}$

$=\left[ M ^{0} L ^{0} T ^0\right]=\text { Dimensionless }$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Similar questions

The unit of Young’s modulus is
Four particles $A, B, C$ and $D$ are moving with constant speed $v$ each. At the instant shown relative velocity of $A$ with respect to $B, C$ and $D$ are in directions
Match List$-I$ with List$-II$

List$-I$ List$-II$
$(a)$ Isothermal $(i)$ Pressure constant
$(b)$ Isochoric $(ii)$ Temperature constant
$(c)$ Adiabatic $(iii)$ Volume constant
$(d)$ Isobaric $(iv)$ Heat content is constant

Choose the correct answer from the options given below

The displacement of a particle varies with time according to the relation : $\text{y}=\text{a}\sin\omega\text{t}+\text{b}\cos\omega\text{t}$
A solid ball of metal has a concentric spherical cavity within it. If the ball is heated, the volume of the cavity will
In the following indicator diagram, the net amount of work done will be
Copper of fixed volume $V$ is drawn into wire of  length $l$. When this wire is subjected to a constant force $F$, the extension produced in the wire is $\Delta l$. Which of the following graphs is a straight line?
A solid sphere (mass $2\ M$) and a thin hollow spherical shell (mass $M$) both of the same size, roll down an inclined plane, then
A vibrating string of certain length $l$ under a tension $T$ resonates with a mode corresponding to the first overtone (third harmonic) of an air column of length $75\, cm$ inside a tube closed at one end. The string also generates $4\, beats$ per second when excited along with a tuning fork of frequency $n$. Now when the tension of the string is slightly increased the number of beats reduces to $2\, per second$. Assuming the velocity of sound in air to be $340\, m/s$, the frequency $n$ of the tuning fork in $Hz$ is
One mole of an ideal gas at $STP$ is heated in an insulated closed container until the average speed of its molecules is doubled. Its pressure would therefore increase by factor.