Small drops of liquid of the same radius coal | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let $n$ be the number of small drops of radius $r$ that coalesce to form a big drop of radius $R$. Here,$n = 2$.By conservation of volume: $n 	im

Vedclass · Accepted Answer

$2^{-\frac{1}{3}}: 1$

Vedclass · Answer

(B) Let $n$ be the number of small drops of radius $r$ that coalesce to form a big drop of radius $R$. Here,$n = 2$.By conservation of volume: $n 	imes (\frac{4}{3} \pi r^3) = \frac{4}{3} \pi R^3$.Substituting $n = 2$: $2r^3 = R^3$,which gives $R = 2^{1/3} r$.The surface energy $E$ is given by $E = T 	imes A$,where $T$ is surface tension and $A$ is surface area.Initial surface energy $E_1 = n 	imes (4 \pi r^2 T) = 2 	imes 4 \pi r^2 T = 8 \pi r^2 T$.Final surface energy $E_2 = 4 \pi R^2 T = 4 \pi (2^{1/3} r)^2 T = 4 \pi (2^{2/3} r^2) T = 4 	imes 2^{2/3} \pi r^2 T$.The ratio of total surface energies after and before the change is $\frac{E_2}{E_1} = \frac{4 	imes 2^{2/3} \pi r^2 T}{8 \pi r^2 T} = \frac{2^{2/3}}{2} = 2^{2/3 - 1} = 2^{-1/3}$.Thus,the ratio is $2^{-1/3} : 1$.

Small drops of liquid of the same radius coalesce to form a big drop. The ratio of the total surface energies after and before the change is:

Similar Questions

$A$ vessel,whose bottom has round holes with a diameter of $0.1 \, mm$,is filled with water. The maximum height to which the water can be filled without leakage is ....... $cm$ (Surface Tension of water = $75 \, dyne/cm$,$g = 1000 \, cm/s^2$).

If a cube of ice is placed in gravity-free space,what happens when the ice melts?

The excess pressure in a soap bubble is double that in another one. The ratio of their volumes is .............

The work done to break a spherical drop of radius $R$ into $n$ drops of equal size is proportional to .............

The pressure inside a soap bubble $A$ is $1.01 \text{ atm}$ and that in a soap bubble $B$ is $1.02 \text{ atm}$. The ratio of the volume of bubble $A$ to that of $B$ is (Surrounding pressure $= 1 \text{ atm}$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module