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,
$\Delta P_{s}=\frac{2 T}{r}=\frac{2 T}{R / 2}=\frac{4 T}{R}$
For bigger drop,
$\Delta P_{b}=\frac{2 T}{R}=\frac{1}{2} \Delta P_{s}$