Question

The surface energy of a liquid drop is $E$. It is sprayed into 1000 equal droplets. Then their surface energy is:

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

Answer 1

The correct option is B $10E$

The surface energy of a droplet is proportional to its surface area. After spraying into 1000 droplets, let the radius of each one will be r.

$\frac{4}{3}\pi R^3=1000\left(\frac{4}{3}\pi r^3\right)$

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

Therefore, surface area of 1000 drops is : $1000\times \left(4\pi r^3\right)=n\left(4\pi R^3\right)$; where $n$ is number of times of original surface area.

Thus, surface area will become $\frac{1000\left(4\pi r^2\right)}{4\pi R^2}=n$ times = $10$ times

As, $E\propto A$

Hence, $E^{\prime }=10E$