Two small drops of liquid of same radius coal | vedclass

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

Question

(C) Let the radius of each small drop be $r$ and the radius of the big drop be $R$.Since the volume remains conserved, the volume of the big drop equa

Vedclass · Accepted Answer

$2^{-1/3} : 1$

Vedclass · Answer

(C) Let the radius of each small drop be $r$ and the radius of the big drop be $R$.Since the volume remains conserved, the volume of the big drop equals the sum of the volumes of the two small drops:$2 	imes (4/3 \pi r^3) = 4/3 \pi R^3$$2r^3 = R^3 \implies R = 2^{1/3}r$.The surface energy $E$ is given by $E = T 	imes A$, where $T$ is surface tension and $A$ is the surface area.$E_{before} = 2 	imes (T 	imes 4\pi r^2) = 8\pi r^2 T$.$E_{after} = T 	imes 4\pi R^2 = 4\pi T (2^{1/3}r)^2 = 4\pi T r^2 2^{2/3}$.The ratio of the total surface energies after and before the change is:$E_{after} / E_{before} = (4\pi T r^2 2^{2/3}) / (8\pi r^2 T) = 2^{2/3} / 2 = 2^{2/3 - 1} = 2^{-1/3}$.Thus, the ratio is $2^{-1/3} : 1$.

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

Similar Questions

Two soap bubbles have different radii but their surface tension is the same. Mark the correct statement.

Pressure inside two soap bubbles are $1.01$ and $1.02$ atmosphere, respectively. The ratio of their volumes is (in $ : 1$)

$A$ drop of water of volume $0.05\, cm^3$ is pressed between two glass plates,as a consequence of which it spreads and occupies an area of $40\, cm^2$. If the surface tension of water is $70\, dyne/cm$,then the normal force required to separate out the two glass plates will be in Newton.

Consider a water droplet of diameter $0.2 \,mm$ where the outside pressure is $1.5 \,N / cm^2$ at $25^{\circ} C$. The pressure inside the droplet, when the surface tension at $25^{\circ} C$ is $0.08 \,N / m$ is

The excess pressure inside the first soap bubble is three times that of a second soap bubble. What is the ratio of the volumes of the first bubble to the second bubble?

Vedclass Test Series

Exam Paper Generator

Online Exam Module