We
are solving series of problems based on the concept surface tension. It is the
property of the liquid because of which the liquid surface behaves like a
stretched elastic membrane. Because of surface tension, liquids always try to
acquire minimum surface area. This is the reason why water drops are spherical
in shape as the sphere has minimum surface area among all possible three
dimensional shapes. Angle of contact is a parameter that measures weather
cohesive or adhesive forces are dominating in a given system. If adhesive
forces are dominating, angle of contact is less than ninety degree and vice versa.Angle of contact is the
angle drawn between two tangents drawn at the point of contact where one
tangent is drawn to the liquid surface and the other tangent is drawn to the
wall of the capillary tube into the liquid. Basing on that there will be
capillarity rise or fall.

**Problem**

When
a capillary tube is immersed in water the mass of water that raised in the tube
is of 5 gram. If the radius of the tube is doubled we need to find the raise of
the water in the new tube and the problem is as shown in the diagram below.

**Solution**

We
know that when a capillary tube is placed in a liquid, a component of surface
tension generates a force that pulls the liquid upward. Simentaniouly we have
liquids weight acting in the downward direction. When this downward force
compensate the upward force due to surface tension, liquid stops rising
further. By equating this two forces, we can solve the problem as shown in the
diagram below.

**Problem**

We
need to find the excess pressure inside an air bubble when the bubble radius is
known to us and surface tension of the liquid is also given to us. Problem is
as shown in the diagram below.

**Solution**

When
the drop is acquiring spherical shape, there is pressure acting towards its
center and it generate excess pressure inside the spherical bubble. Basing on
the formula that we have derived, we can solve the problem as shown in the
diagram below.

**Problem**

Surface
area and surface tension of the liquid is given to us in the problem as shown
in the diagram below. We need to find the excess pressure inside the drop.

**Solution**

We
know the surface area of the sphere and hence we can express the radius of the
drop in terms of area of cross section as shown in the diagram below.
Substituting that data in the excess pressure formula, we can solve the problem
as shown in the diagram below.

**Problem**

Two
soap bubbles are combined to form a single bubble. In this process change in
volume and area is given to us in the problem. Pressure and surface tension are
given to us and we need to find the relation between them.

**Solution**

We
know that under isothermal conditions, Boyle's law is valid and we can equate
product of pressure and volume is conserved as shown in the diagram below. By
applying the formula for the pressure and the volume of the sphere we can solve
the problem as shown in the diagram below.

**Problem**

A
thread of length L is placed on a soap film of known surface tension. If the
film is pierced with a needle we need to measure the tension in that thread and
the problem is as shown in the diagram below.

**Solution**

We
can equate the force due to surface tension to the force and centripetal force
and solve the problem as shown in the diagram below.

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