Question

A drop of water of mass $m$ , surface tension $T$ , is trapped between two parallel glass plates, separated by distance $d$ . The force needed to separate the plates, to pull them apart, perpendicular to the plane of plates, is

• A. $\frac{2Tm}{\pi d^2\rho }$
• B. $\frac{2Tm}{d^2\rho }$
• C. $\frac{Tm}{2d^2\rho }$
• D. $\frac{Tm}{2\pi d^2\rho }$

Answer 1

Answer: (B)

Pressure inside the liquid film is smaller than outside by
$\Delta P=\frac{T}{r}=\frac{Tcos\theta }{\frac{d}{2}}=\frac{2Tcos\theta }{d},$
$F=\Delta P\times A=A\times \frac{2Tcos\theta }{d}$
$m=A\times d\times \rho \Rightarrow A=\frac{m}{d\times \rho }$
$\Rightarrow F=\frac{2Tcos\theta }{d}\times \frac{m}{d\rho }=\frac{2Tmcos\theta }{d^2\rho }$
$\Rightarrow F=\frac{2Tm}{d^2\cdot \rho }$