“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 r1 and r2 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 cosθ
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, h1/h2 = r2/r1
= 2 : 1
(2) If the excess pressure
inside a soap bubble of radius r1
in air is equal to the excess pressure inside air bubble of radius r2 inside the soap solution,
then r1 : r2 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 4S/r where as the excess pressure
inside an air bubble in the soap solution is 2S/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 2S/r and not 4S/r. Remember that in the case of a soap bubble in air there are two liquid surfaces].
As given in the question, we have
4S/r1 = 2S/r2
This gives r1/r2 = 2
Or, r1
: r2 = 2 : 1
