Question

A film soap solution is made in a rectangular frame of length 10cm and breadth 4cm. The force of surface tension on the smaller edge of the frame is ……. Dyne. (Surface tension of soap solution= 30 dyne/cm)
(A) 60
(B) 120
(C) 300
(D) 240

Answer 1

Hint: Surface tension is defined as the force per unit length or energy per unit area. Surface tension allows the liquid-air surface to shrink in a minimum area. Mainly it arises due to the difference between adhesion and cohesion forces on the boundary of the mediums. So, mathematically
\[T = \dfrac{F}{l}\]
For a soap solution, the interface of soap solution-air is on both sides of the soap solution unlike water, so
\[T = \dfrac{F}{{2l}}\]

Complete step by step answer:
-Surface tension is the property of a liquid which resists an external force due to the cohesion nature of its molecules. On a boundary of liquid and air, the molecules on the top surface face only the inward cohesive force of its molecules while the molecules in the bulk face this force equally from all its side.
-Due to the difference in the cohesive force of liquid molecules and adhesive force of liquid molecules and air molecules, a net force acts on the boundary molecules either into the liquid or away from it. Generally, the cohesive force is greater than the adhesive force. To calculate the surface tension, we need to find the maximum force the liquid-air boundary can take and divide it by the length of the boundary.
-For a soap solution, the interface of soap solution-air is on both sides of the soap solution unlike water, so
\[
T = \dfrac{F}{{2l}} \\
\Rightarrow F = T.2l \\
\]
Substituting the values for the shorter boundary i.e. along the breadth,
\[
\Rightarrow F = 30(2 \times 4) \\
\therefore F = 240 dyne \\
\]
The correct answer is option D.

Note:Be careful in surface tension problems regarding the length of the surface. When a liquid is mentioned then there will be only one surface so length is L. For ex- water in cup. For films like soap solution it has two surfaces exposed to air on either side so length will be 2L.