Question

Two glass plates are separated by water. If surface tension of water is $75$ dyne/cm and area of each plate wetted by water is $8\, cm ^{2}$ and the distance between the plates is $0.12 \,mm$, then the force applied to separate the two plates is

• A. $ 10^2$ dyne
• B. $ 10^4$ dyne
• C. $10^5$ dyne
• D. $10^6$ dyne

Answer 1

Answer: (C)

The shape of water layer between the two plates is shown in the figure.
Thickness $d$ of the film $=0.12\, mm$
$=0.012\, cm$
Radius $R$ of the cylindrical face $=\frac{d}{2}$
Pressure difference across the surface
$=\frac{T}{R}=\frac{2 T}{d}$
Area of each plate wetted by water $=A$
Force $F$ required to separate the two plates is given by
$F=$ pressure difference $ \times $ area
$=\frac{2 T}{d} A$
Putting the given values, we get
$F=\frac{2 \times 75 \times 8}{0.012}=10^{5} $ dyne