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. $\frac{2 T m}{\pi d^{2} \rho }$
• B. $\frac{2 T m}{d^{2} \rho }$
• C. $\frac{T m}{2 d^{2} \rho }$
• D. $\frac{T m}{2 \pi d^{2} \rho }$

Answer 1

Answer: (B)

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