“It doesn't
matter how beautiful your theory is; it doesn't matter how smart you are. If it
doesn't agree with experiment, it's wrong.”

–
Richard Feynman

Two questions on surface tension were included in
the KEAM (Engineering) 2012 question paper. Here are the questions with
solution:

(1) If two capillary tubes
of radii

*r*_{1}and*r*_{2}in the ratio 1 : 2 are dipped vertically in water, then the ratio of capillary rises in the respective tubes is
(a) 1 : 4

(b) 4 : 1

(c) 1 : 2

(d) 2 : 1

(e) 1 : √2

The capillary rise

*h*due to surface tension is relate to the surface tension*S*as*S = hrρg/*2 cos

*θ*

where

*r*is the radius of the capillary tube,*ρ*is the density of the liquid,*g*is the acceleration due to gravity and*θ*is the angle of contact.
Evidently

*h*is*inversely*proportional to*r*.
Therefore,

*h*_{1}/*h*_{2}=*r*_{2}/*r*_{1}= 2 : 1
(2) If the excess pressure
inside a soap bubble of radius

*r*_{1}in air is equal to the excess pressure inside air bubble of radius*r*_{2}inside the soap solution, then*r*_{1}:*r*_{2}is
(a) 2 : 1

(b) 1 : 2

(c) 1 : 4

(d) √2 : 1

(e) 1 : √2

The excess pressure inside a soap bubble in air
is 4

*S/r*where as the excess pressure inside an air bubble in the soap solution is 2*S/r*where*S*is the surface tension (of soap solution) and*r*is the radius of the bubble.
[In the case of the air bubble in the soap
solution there is one liquid surfaoe only and that is why the excess pressure
is 2

*S/r*and not 4*S/r*. Remember that in the case of a soap bubble in air there are*two*liquid surfaces].
As given in the question, we have

4

*S/r*_{1}*=*2*S/r*_{2}
This gives

*r*_{1}/*r*_{2}= 2
Or,

*r*_{1}:*r*_{2}= 2 : 1
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