The work done to break a spherical drop of ra | vedclass

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

Question

(C) The volume of the liquid remains constant during the process.Let $R$ be the radius of the large drop and $r$ be the radius of each of the $n$ smal

Vedclass · Accepted Answer

$n^{1/3} - 1$

Vedclass · Answer

(C) The volume of the liquid remains constant during the process.Let $R$ be the radius of the large drop and $r$ be the radius of each of the $n$ small drops.Volume of large drop = $n 	imes$ Volume of small drop$\frac{4}{3} \pi R^3 = n 	imes \frac{4}{3} \pi r^3$$R^3 = n r^3 \implies r = \frac{R}{n^{1/3}}$The work done $W$ is equal to the increase in surface energy:$W = S 	imes \Delta A = S 	imes (A_{final} - A_{initial})$$W = S 	imes (n 	imes 4 \pi r^2 - 4 \pi R^2)$Substitute $r = R n^{-1/3}$:$W = S 	imes 4 \pi (n 	imes (R n^{-1/3})^2 - R^2)$$W = S 	imes 4 \pi R^2 (n 	imes n^{-2/3} - 1)$$W = 4 \pi R^2 S (n^{1/3} - 1)$Since $4 \pi R^2 S$ is constant,the work done is proportional to $(n^{1/3} - 1)$.

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

Similar Questions

If the excess pressure inside a soap bubble of radius $3 \,mm$ is equal to the pressure of a water column of height $0.8 \,cm$, then the surface tension of the soap solution is ( $\rho_{\text{water}} = 1000 \,kg/m^3, g = 9.8 \,m/s^2$ ).

Pure water rises through a height $h$ in a capillary tube of internal radius $r$. Surface tension of water is $T$. The pressure difference between the water level in the container and the lowest point of the concave meniscus is

Two small drops of mercury,each of radius $R$,coalesce to form a single large drop. The ratio of the total surface energies before and after the change is

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

$A$ capillary tube of radius $r$ is dipped in a liquid of density $\rho$ and surface tension $S$. If the angle of contact is $\theta$,what is the pressure difference between the two surfaces in the beaker and the capillary?

Vedclass Test Series

Exam Paper Generator

Online Exam Module