CBSE Class 11 Physics Chapter 10: Mechanical Properties of Fluids NCERT Solutions

The pressure exerted by a fluid at rest is given by the hydrostatic pressure formula: P = h\rho g, where P is the pressure, h is the height of the fluid column, \rho is the density of the fluid, and g is the acceleration due to gravity.

a) Blood Pressure at Feet vs. Brain:

Blood pressure is influenced by the height of the blood column within the body. Since the feet are at a lower position than the brain, the height of the blood column from the heart to the feet is greater than the height from the heart to the brain. According to the formula P = h\rho g, pressure is directly proportional to height (h). Therefore, the blood pressure is greater at the feet compared to the brain due to this difference in height.

b) Atmospheric Pressure Variation with Altitude:

The density of air is highest near the Earth's surface (sea level) and decreases significantly as altitude increases. Atmospheric pressure is essentially the weight of the air column above a certain point. As the air becomes less dense at higher altitudes, the weight of the air column above decreases. At a height of about 6 km, the density of air has reduced considerably, causing the atmospheric pressure to drop to approximately half of its value at sea level, even though the atmosphere extends much higher.

c) Hydrostatic Pressure as a Scalar:

While pressure is defined as force per unit area (P = F/A), and force is a vector, hydrostatic pressure in a fluid at rest is a scalar quantity. This is because, according to Pascal's principle, pressure applied to an enclosed fluid is transmitted undiminished to every portion of the fluid and the walls of the containing vessel, in all directions. At any point within the fluid, the pressure acts equally in all directions, meaning it does not have a specific direction associated with it, making it a scalar quantity.

The angle of contact (\theta) is defined as the angle between the tangent to the liquid surface at the point of contact and the solid surface inside the liquid. It is determined by the balance of interfacial tensions: S_{la} (liquid-air), S_{sa} (solid-air), and S_{sl} (solid-liquid). The equilibrium condition at the line of contact is given by S_{sa} = S_{sl} + S_{la} \cos\theta.

a) Angle of Contact: Mercury vs. Water with Glass:

For mercury on glass, the cohesive forces (attraction between mercury molecules) are stronger than the adhesive forces (attraction between mercury and glass). This results in a large S_{sl} value relative to S_{la}, leading to a large \cos\theta and thus an obtuse angle of contact (\theta > 90^\circ). Conversely, for water on glass, the adhesive forces are stronger than the cohesive forces. This means S_{sl} is smaller, leading to a smaller \cos\theta and an acute angle of contact (\theta < 90^\circ).

b) Wetting Behavior: Water vs. Mercury on Glass:

Water wets glass because the adhesive forces between water and glass are stronger than the cohesive forces within water. This causes the water to spread out, minimizing the S_{sl} interface and resulting in an acute angle of contact. Mercury does not wet glass because its cohesive forces are stronger than the adhesive forces with glass. This causes mercury to minimize its contact with the glass surface, forming drops and exhibiting an obtuse angle of contact.

c) Surface Tension Independence of Surface Area:

Surface tension is an intrinsic property of a liquid that arises from the cohesive forces between its molecules. It represents the force per unit length acting along the surface, or the energy per unit area required to increase the surface area. While surface tension does work to minimize surface area, the value of surface tension itself (force per unit length or energy per unit area) does not change with the size or area of the surface, provided the conditions like temperature remain constant.

d) Detergents and Angle of Contact:

Detergents reduce the surface tension of water. They also alter the adhesive forces between water and the surface being cleaned. By reducing surface tension and often increasing adhesion, detergents help water spread out more effectively on surfaces, leading to a smaller angle of contact. This allows the water and detergent solution to penetrate fabrics and lift dirt more efficiently.

e) Spherical Shape of Liquid Drops:

In the absence of external forces like gravity, a liquid drop assumes a spherical shape because surface tension tends to minimize the surface area for a given volume. A sphere has the smallest surface area to volume ratio among all possible shapes. By forming a sphere, the liquid minimizes the potential energy associated with its surface, achieving a stable configuration.