Question

The surface energy of a liquid drop is $u$ it is sprayed into $1000$ equal droplets, then the total surface energy becomes

• A. $u$
• B. $10u$
• C. $100u$
• D. $1000u$

Answer 1

The correct option is B

$10u$

The explanation for the correct answer:

Step 1:Given parameters:

The surface energy of a liquid drop = $u$

Step 3:Solution:

the surface energy of a liquid drop is given as,

$u=T\times 4{\mathrm{\pi R}}^2$ , here $T$ is the surface tension of the liquid and $R$ is the initial radius of the liquid before splitting

when the liquid drop is sprayed into 1000 droplets each of radius r, then

$Thevolumeofonedrop=totalvolumeof1000droplets$

$\frac{4}{3}{\mathrm{\pi R}}^3=1000\times \frac{4}{3}\pi r^3$

$r=\frac{R}{10}$

then,

$u^{\text{'}}=1000\times T\times 4\pi r^2$

$u^{\text{'}}=1000\times T\times 4\pi {\left(\frac{R}{10}\right)}^2$

$u^{\text{'}}=10\times (T\times 4\pi R^2)$

$u^{\text{'}}=10u$

Hence,

the total surface energy becomes $10u$.

Hence, Option B is correct.