Question

A water drop is divided into $8$ equal droplets. The pressure difference between the inner and outer side of the big drop will be

• A. same as for smaller droplet
• B. $\frac{1}{2}$ of that for smaller droplet
• C. $\frac{1}{4}$ of that for smaller droplet
• D. twice that for smaller droplet

Answer 1

Answer: (B)

Volume of big drop $=$ Volume of $8$ droplets ie,
$\frac{4}{3}\pi R^3=8\times \frac{4}{3}\pi r^3$
$\therefore r=\frac{R}{2}$
For smaller drop,
$\Delta P_s=\frac{2T}{r}=\frac{2T}{R/2}=\frac{4T}{R}$
For bigger drop,
$\Delta P_b=\frac{2T}{R}=\frac{1}{2}\Delta P_s$