Two mercury drops of radii r and 2r merge to | vedclass

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

Question

(D) Initial surface area $A_i = 4 \pi r^2 + 4 \pi (2r)^2 = 4 \pi r^2 + 16 \pi r^2 = 20 \pi r^2$.Initial surface energy $E_i = A_i S = 20 \pi r^2 S$.Vo

Vedclass · Accepted Answer

$2.7$

Vedclass · Answer

(D) Initial surface area $A_i = 4 \pi r^2 + 4 \pi (2r)^2 = 4 \pi r^2 + 16 \pi r^2 = 20 \pi r^2$.Initial surface energy $E_i = A_i S = 20 \pi r^2 S$.Volume conservation: $\frac{4}{3} \pi r^3 + \frac{4}{3} \pi (2r)^3 = \frac{4}{3} \pi R^3$.$r^3 + 8r^3 = R^3 \implies R^3 = 9r^3 \implies R = 9^{1/3} r$.Final surface area $A_f = 4 \pi R^2 = 4 \pi (9^{1/3} r)^2 = 4 \pi (9^{2/3}) r^2$.Given $9^{2/3} = 4.326$,so $A_f = 4 \pi (4.326) r^2 = 17.304 \pi r^2$.Final surface energy $E_f = 17.304 \pi r^2 S$.Energy released $\Delta E = E_i - E_f = 20 \pi r^2 S - 17.304 \pi r^2 S = 2.696 \pi r^2 S \approx 2.7 \pi r^2 S$.

Two mercury drops of radii $r$ and $2r$ merge to form a bigger drop. The surface energy released in the process is nearly (Surface tension of mercury is $S$ and take $9^{2/3} = 4.326$). (in $\pi r^2 S$)

Similar Questions

In an isothermal process,$2$ water drops of radius $1 \, mm$ are combined to form a bigger drop. Find the energy change (in $\mu J$) in this process if the surface tension $T = 0.1 \, N/m$.

The surface tension of soap solution is $0.03 \,N/m$. The work done in blowing to form a soap bubble of surface area $40 \,cm^2$ (in $J$) is:

The surface energy of a liquid drop is $V$. It is sprayed into $1000$ equal droplets. The surface energy of all the droplets is

$A$ mercury drop of radius $1 \ cm$ is sprayed into $10^6$ drops of equal size. The energy expended in joules is (surface tension of mercury is $460 \times 10^{-3} \ N/m$).

$A$ water drop of radius $1\,cm$ is broken into $729$ equal droplets. If the surface tension of water is $75\,dyne/cm$,then the gain in surface energy up to the first decimal place will be $...\times 10^{-4}\,J$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module