Question

The surface energy of a liquid drop is $u$. It is sprayed into $1000$ equal droplets. Then its surface energy, becomes

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

Answer 1

The correct option is B $10u$

Surface energy is defined as the amount of work done in increasing the area of the surface film through unity. So it's proportional to the surface area of the film.

Now it's given that the surface energy of a liquid drop is $u$ and it's subdivided into 1000 equal droplets. In this process, the volume of the liquid will remain constant or unchanged but the newly formed 1000 drops will have different surface area than the original drop. Hence there will be a change in surface area, hence the surface energy will also be changed proportionally.

$\Rightarrow$ Volume of original drop = $1000\times$ Volume of one drop

Let the radius of the original drop be $R$ and of the newly formed droplet is $r$.

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

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

The surface area of the original liquid drop is $4\pi R^2$ and of the newly formed $1000$ liquid drops is $(1000\times 4\pi r^2)$

We know that $r=\frac{R}{10}$, so area of $1000$ liquid drops $=1000\times 4\pi (\frac{R}{10}{)}^2=10\times 4\pi R^2$

As we know that surface energy of a liquid drop is directly proportional to it's surface area, and the surface area becomes $10$ times the original surface area, hence the surface energy will also become $10$ times the original surface energy or $10u$

Hence the surface energy becomes $10u$ So the Correct answer is $B$.