NCERT Solutions
Class 11 Physics
Mechanical Properties of Fluids

Q. 9.2
Explain why
(a) The angle of contact of mercury with glass is obtuse, while that of water with glass is acute.
(b) Water on a clean glass surface tends to spread out while mercury on the same surface tends to form drops. (Put differently, water wets glass while mercury does not.)
(c) Surface tension of a liquid is independent of the area of the surface
(d) Water with detergent dissolved in it should have small angles of contact.
(e) A drop of liquid under no external forces is always spherical in shape
The angle between the tangent to the liquid surface at the point of contact and the surface inside the liquid is called the angle of contact (θ), as shown in the given figure.
Sla = interfacial tensions between the liquid-air,
Ssa interfacial tensions between the solid-air and
Ssl = interfacial tensions between the liquid-air
At the line of contact, the surface forces between the three media must be in equilibrium, i.e.
cos θ = (Ssa - Ssl)/ (Sla)
The angle of contact θ, is obtuse if Ssa < Sla (as in the case of mercury on glass). This angle is acute if Ssl < Sla (as in the case of water on glass).
- Explanation: - Mercury molecules (which make an obtuse angle with glass) have a strong force of attraction between themselves and a weak force of attraction toward solids. Hence, they tend to form drops.
- Explanation: - For equilibrium of a liquid drop on the surface of a solid, the equation TSA = TSL + TLA cos θ ... (i) must be true.
For mercury-glass, angle of contact is obtuse. In order to achieve this obtuse value of angle of contact, the mercury tends to form a drop.
- Explanation: - Surface tension is the force acting per unit length at the interface between the plane of a liquid and any other surface. This force is independent of the area of the liquid surface. Hence, surface tension is also independent of the area of the liquid surface.
- Explanation: - As the cloth has narrow spaces in the form of fine capillaries. The rise of liquid in a capillary tube is given by:-
h = (2Scos (θ).)/ (rρ g);
=> h ∝ cos (θ). It shows that if θ is small, cos θ will be large and as a result detergent raises more in fine capillaries in the cloth.
As detergents having small angles of contact, therefore they can penetrate more, so will remove dirt from the cloth.
(e) Explanation: - In the absence of external forces, only force acting on the liquid drop is due to surface tension. A drop of liquid tends to acquire minimum surface area due to the property of surface tension. Since for a given volume of liquid, surface area is least for a sphere. So the liquid drop will always assume a spherical shape.