Find the best tutors and institutes for Class 11 Tuition
Q10.2(b):
Explain why (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.)
Solution :
1. Theoretical Foundation: The Mechanics of Adhesion and Cohesion
The wetting behavior of a liquid on a solid surface is determined by the competition between two specific molecular forces:
- Cohesive Forces ($F_c$): The intermolecular forces of attraction between molecules of the same substance.
- Adhesive Forces ($F_a$): The intermolecular forces of attraction between molecules of different substances (in this case, the liquid molecules and the glass surface molecules).
[Per the Young-Dupré equation and the concept of Surface Tension, the equilibrium shape of a drop is governed by the contact angle $\theta$.]
2. Comparative Analysis of Intermolecular Dynamics
| Characteristic | Water-Glass Interaction | Mercury-Glass Interaction |
|---|---|---|
| Dominant Force | $F_a > F_c$ | $F_c > F_a$ |
| Contact Angle ($\theta$) | Acute ($\theta < 90^\circ$) | Obtuse ($\theta > 90^\circ$) |
| Surface Result | Spreading (Wetting) | Droplet Formation (Non-wetting) |
3. Mathematical Logic of Surface Energy
The shape of the liquid interface minimizes the total surface energy of the system. The total energy $E$ is given by:
$E = \gamma_{sl} A_{sl} + \gamma_{sg} A_{sg} + \gamma_{lg} A_{lg}$
Where $\gamma$ represents the interfacial tension between Solid-Liquid ($sl$), Solid-Gas ($sg$), and Liquid-Gas ($lg$).
[By the Principle of Minimum Potential Energy]:
- For water, the adhesion to glass is strong enough to reduce the energy of the solid-liquid interface effectively, causing the liquid to maximize the surface area of contact, thus spreading out.
- For mercury, the cohesive forces within the mercury atoms are significantly stronger than the adhesive force to the glass. To minimize energy, the mercury atoms maximize their contact with each other (forming a sphere, the shape with the minimum surface area for a given volume) and minimize contact with the glass, resulting in bead formation.
4. Visual Representation of Contact Angles
5. Conclusion
The wetting of a surface is a function of the contact angle $\theta$. When $F_a > F_c$, the contact angle is acute, leading to wetting. When $F_c > F_a$, the contact angle is obtuse, leading to the formation of a spherical drop to minimize surface area and energy.
Final Solution: Water spreads on a clean glass surface because the adhesive forces between water molecules and glass molecules are stronger than the cohesive forces between water molecules. Conversely, mercury forms drops because the cohesive forces between mercury atoms are far stronger than the adhesive forces between mercury and glass.
More Questions from Class 11 Physics Mechanical Properties of Fluids EXERCISES
- Q9.1(a): Explain why (a) The blood pressure in humans is greater at the feet than at the brain
- Q9.1(b): Explain why (b) Atmospheric pressure at a height of about (6\text{ km}) decreases to nearly half of its value at the sea level, though the height of the atmosphere is more than (100\text{ km})
- Q9.1(c): Explain why (c) Hydrostatic pressure is a scalar quantity even though pressure is force divided by area.
- Q9.10: If (15.0\text{ cm}) of water and spirit each are further poured into the respective arms of the tube, what is the difference in the levels of mercury in the two arms ? (Specific gravity of mercury = (13.6))
- Q9.11: Can Bernoulli’s equation be used to describe the flow of water through a rapid in a river ? Explain.
- Q9.12: Does it matter if one uses gauge instead of absolute pressures in applying Bernoulli’s equation ? Explain.
- Q9.13: Glycerine flows steadily through a horizontal tube of length (1.5\text{ m}) and radius (1.0\text{ cm}). If the amount of glycerine collected per second at one end is (4.0 \times 10^{-3}\text{ kg s}^{-1}), what is the pressure difference between the two ends of the tube ? (Density of glycerine = (1.3 \times 10^{3}\text{ kg m}^{-3}) and viscosity of glycerine = (0.83\text{ Pa s})). [You may also like to check if the assumption of laminar flow in the tube is correct].
- Q9.14: In a test experiment on a model aeroplane in a wind tunnel, the flow speeds on the upper and lower surfaces of the wing are (70\text{ m s}^{-1})and (63\text{ m s}^{-1}) respectively. What is the lift on the wing if its area is (2.5\text{ m}^{2}) ? Take the density of air to be (1.3\text{ kg m}^{-3}).
- Q9.15: Figures 9.20(a) and (b) refer to the steady flow of a (non-viscous) liquid. Which of the two figures is incorrect ? Why ?
- Q9.16: The cylindrical tube of a spray pump has a cross-section of (8.0\text{ cm}^{2}) one end of which has (40) fine holes each of diameter (1.0\text{ mm}). If the liquid flow inside the tube is (1.5\text{ m min}^{-1}), what is the speed of ejection of the liquid through the holes ?
- Q9.17: A U-shaped wire is dipped in a soap solution, and removed. The thin soap film formed between the wire and the light slider supports a weight of (1.5 \times 10^{-2}\text{ N}) (which includes the small weight of the slider). The length of the slider is (30\text{ cm}). What is the surface tension of the film ?
- Q9.18: Figure 9.21 (a) shows a thin liquid film supporting a small weight = (4.5 \times 10^{-2}\text{ N}). What is the weight supported by a film of the same liquid at the same temperature in Fig. (b) and (c) ? Explain your answer physically.
- Q9.19: What is the pressure inside the drop of mercury of radius (3.00\text{ mm}) at room temperature ? Surface tension of mercury at that temperature ((20^{\circ}\text{C})) is (4.65 \times 10^{-1}\text{ N m}^{-1}). The atmospheric pressure is (1.01 \times 10^{5}\text{ Pa}). Also give the excess pressure inside the drop.
- Q9.2(a): Explain why (a) The angle of contact of mercury with glass is obtuse, while that of water with glass is acute.
- Q9.2(b): Explain why (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.)
- Q9.2(c): Explain why (c) Surface tension of a liquid is independent of the area of the surface
- Q9.2(d): Explain why (d) Water with detergent disolved in it should have small angles of contact.
- Q9.2(e): Explain why (e) A drop of liquid under no external forces is always spherical in shape
- Q9.20: What is the excess pressure inside a bubble of soap solution of radius (5.00\text{ mm}), given that the surface tension of soap solution at the temperature ((20^{\circ}\text{C})) is (2.50 \times 10^{-2}\text{ N m}^{-1}) ? If an air bubble of the same dimension were formed at depth of (40.0\text{ cm}) inside a container containing the soap solution (of relative density (1.20)), what would be the pressure inside the bubble ? (1 atmospheric pressure is (1.01 \times 10^{5}\text{ Pa})).
- Q9.3(a): Fill in the blanks using the word(s) from the list appended with each statement: (a) Surface tension of liquids generally . . . with temperatures (increases / decreases)
- Q9.3(b): Fill in the blanks using the word(s) from the list appended with each statement: (b) Viscosity of gases . . . with temperature, whereas viscosity of liquids . . . with temperature (increases / decreases)
- Q9.3(c): Fill in the blanks using the word(s) from the list appended with each statement: (c) For solids with elastic modulus of rigidity, the shearing force is proportional to . . . , while for fluids it is proportional to . . . (shear strain / rate of shear strain)
- Q9.3(d): Fill in the blanks using the word(s) from the list appended with each statement: (d) For a fluid in a steady flow, the increase in flow speed at a constriction follows (conservation of mass / Bernoulli’s principle)
- Q9.3(e): Fill in the blanks using the word(s) from the list appended with each statement: (e) For the model of a plane in a wind tunnel, turbulence occurs at a ... speed for turbulence for an actual plane (greater / smaller)
- Q9.4(a): Explain why (a) To keep a piece of paper horizontal, you should blow over, not under, it
- Q9.4(b): Explain why (b) When we try to close a water tap with our fingers, fast jets of water gush through the openings between our fingers
- Q9.4(c): Explain why (c) The size of the needle of a syringe controls flow rate better than the thumb pressure exerted by a doctor while administering an injection
- Q9.4(d): Explain why (d) A fluid flowing out of a small hole in a vessel results in a backward thrust on the vessel
- Q9.4(e): Explain why (e) A spinning cricket ball in air does not follow a parabolic trajectory
- Q9.5: A (50\text{ kg}) girl wearing high heel shoes balances on a single heel. The heel is circular with a diameter (1.0\text{ cm}). What is the pressure exerted by the heel on the horizontal floor ?
- Q9.6: Toricelli’s barometer used mercury. Pascal duplicated it using French wine of density (984\text{ kg m}^{-3}). Determine the height of the wine column for normal atmospheric pressure.
- Q9.7: A vertical off-shore structure is built to withstand a maximum stress of (10^{9}\text{ Pa}). Is the structure suitable for putting up on top of an oil well in the ocean ? Take the depth of the ocean to be roughly (3\text{ km}), and ignore ocean currents.
- Q9.8: A hydraulic automobile lift is designed to lift cars with a maximum mass of (3000\text{ kg}). The area of cross-section of the piston carrying the load is (425\text{ cm}^{2}). What maximum pressure would the smaller piston have to bear ?
- Q9.9: A U-tube contains water and methylated spirit separated by mercury. The mercury columns in the two arms are in level with (10.0\text{ cm}) of water in one arm and (12.5\text{ cm}) of spirit in the other. What is the specific gravity of spirit ?
- Q10.1(a): Explain why (a) The blood pressure in humans is greater at the feet than at the brain
- Q10.1(b): Explain why (b) Atmospheric pressure at a height of about 6 km decreases to nearly half of its value at the sea level, though the height of the atmosphere is more than 100 km
- Q10.1(c): Explain why (c) Hydrostatic pressure is a scalar quantity even though pressure is force divided by area.
- Q10.10: In the previous problem, if 15.0 cm of water and spirit each are further poured into the respective arms of the tube, what is the difference in the levels of mercury in the two arms ? (Specific gravity of mercury = 13.6)
- Q10.11: Can Bernoulli’s equation be used to describe the flow of water through a rapid in a river ? Explain.
- Q10.12: Does it matter if one uses gauge instead of absolute pressures in applying Bernoulli’s equation ? Explain.
- Q10.13: Glycerine flows steadily through a horizontal tube of length 1.5 m and radius 1.0 cm. If the amount of glycerine collected per second at one end is $4.0 \times 10^{-3} kg s^{-1}$, what is the pressure difference between the two ends of the tube ? (Density of glycerine = $1.3 \times 10^3 kg m^{-3}$ and viscosity of glycerine = $0.83 Pa s$). [You may also like to check if the assumption of laminar flow in the tube is correct].
- Q10.14: In a test experiment on a model aeroplane in a wind tunnel, the flow speeds on the upper and lower surfaces of the wing are $70 m s^{-1}$ and $63 m s^{-1}$ respectively. What is the lift on the wing if its area is $2.5 m^2$ ? Take the density of air to be $1.3 kg m^{-3}$.
- Q10.15: Figures 10.23(a) and (b) refer to the steady flow of a (non-viscous) liquid. Which of the two figures is incorrect ? Why ?
- Q10.16: The cylindrical tube of a spray pump has a cross-section of $8.0 cm^2$ one end of which has 40 fine holes each of diameter 1.0 mm. If the liquid flow inside the tube is $1.5 m min^{-1}$, what is the speed of ejection of the liquid through the holes ?
- Q10.17: A U-shaped wire is dipped in a soap solution, and removed. The thin soap film formed between the wire and the light slider supports a weight of $1.5 \times 10^{-2} N$ (which includes the small weight of the slider). The length of the slider is 30 cm. What is the surface tension of the film ?
- Q10.18: Figure 10.24 (a) shows a thin liquid film supporting a small weight = $4.5 \times 10^{-2} N$. What is the weight supported by a film of the same liquid at the same temperature in Fig. (b) and (c) ? Explain your answer physically.
- Q10.19: What is the pressure inside the drop of mercury of radius 3.00 mm at room temperature ? Surface tension of mercury at that temperature (20 °C) is $4.65 \times 10^{-1} N m^{-1}$. The atmospheric pressure is $1.01 \times 10^5 Pa$. Also give the excess pressure inside the drop.
- Q10.2(a): Explain why (a) The angle of contact of mercury with glass is obtuse, while that of water with glass is acute.
- Q10.2(c): Explain why (c) Surface tension of a liquid is independent of the area of the surface
- Q10.2(d): Explain why (d) Water with detergent disolved in it should have small angles of contact.
- Q10.2(e): Explain why (e) A drop of liquid under no external forces is always spherical in shape
- Q10.20: What is the excess pressure inside a bubble of soap solution of radius 5.00 mm, given that the surface tension of soap solution at the temperature (20 °C) is $2.50 \times 10^{-2} N m^{-1}$ ? If an air bubble of the same dimension were formed at depth of 40.0 cm inside a container containing the soap solution (of relative density 1.20), what would be the pressure inside the bubble ? (1 atmospheric pressure is $1.01 \times 10^5 Pa$).
- Q10.3(a): Fill in the blanks using the word(s) from the list appended with each statement: (a) Surface tension of liquids generally . . . with temperatures (increases / decreases)
- Q10.3(b): Fill in the blanks using the word(s) from the list appended with each statement: (b) Viscosity of gases . . . with temperature, whereas viscosity of liquids . . . with temperature (increases / decreases)
- Q10.3(c): Fill in the blanks using the word(s) from the list appended with each statement: (c) For solids with elastic modulus of rigidity, the shearing force is proportional to . . . , while for fluids it is proportional to . . . (shear strain / rate of shear strain)
- Q10.3(d): Fill in the blanks using the word(s) from the list appended with each statement: (d) For a fluid in a steady flow, the increase in flow speed at a constriction follows (conservation of mass / Bernoulli’s principle)
- Q10.3(e): Fill in the blanks using the word(s) from the list appended with each statement: (e) For the model of a plane in a wind tunnel, turbulence occurs at a ... speed for turbulence for an actual plane (greater / smaller)
- Q10.4(a): Explain why (a) To keep a piece of paper horizontal, you should blow over, not under, it
- Q10.4(b): Explain why (b) When we try to close a water tap with our fingers, fast jets of water gush through the openings between our fingers
- Q10.4(c): Explain why (c) The size of the needle of a syringe controls flow rate better than the thumb pressure exerted by a doctor while administering an injection
- Q10.4(d): Explain why (d) A fluid flowing out of a small hole in a vessel results in a backward thrust on the vessel
- Q10.4(e): Explain why (e) A spinning cricket ball in air does not follow a parabolic trajectory
- Q10.5: A 50 kg girl wearing high heel shoes balances on a single heel. The heel is circular with a diameter 1.0 cm. What is the pressure exerted by the heel on the horizontal floor ?
- Q10.6: Toricelli’s barometer used mercury. Pascal duplicated it using French wine of density 984 $kg m^{-3}$. Determine the height of the wine column for normal atmospheric pressure.
- Q10.7: A vertical off-shore structure is built to withstand a maximum stress of $10^9$ Pa. Is the structure suitable for putting up on top of an oil well in the ocean ? Take the depth of the ocean to be roughly 3 km, and ignore ocean currents.
- Q10.8: A hydraulic automobile lift is designed to lift cars with a maximum mass of 3000 kg. The area of cross-section of the piston carrying the load is $425 cm^2$. What maximum pressure would the smaller piston have to bear ?
- Q10.9: A U-tube contains water and methylated spirit separated by mercury. The mercury columns in the two arms are in level with 10.0 cm of water in one arm and 12.5 cm of spirit in the other. What is the specific gravity of spirit ?
CBSE Solutions for Class 11 Physics Mechanical Properties of Fluids
Chapters in CBSE - Class 11 Physics
Top Tutors who teach Mechanical Properties of Fluids
Top Tutor
Bajaj Nagar, Nagpur
3 yrs of
Exp
Online Classes
Student's Home
Only the students attitude makes a subject HARD or EASY. FUNDAMENTALS are the only need for all Competitive Exams. Once you GET it, cant be bothered again.
Super Tutor
Malkajgiri D.D.Colony, Hyderabad
20 yrs of
Exp
7 students
1600 hrs of classes completed
500
per hour
Online Classes
I was teaching SSC and CBSE students of Grade 11. I have more than 12 years of experiance in teaching Class 11 Mathematics. Prepared additional resources using various other state syllabus course contents. Conducted regular tests at the end of each topic. Conducted additional quizzes and examinations for each term. Slow-learners are given special attention through providing additional learning materials and resources.
The tutor's explanation is clear, concise and relatable. Greatly improved my understanding and confidence in math. Highly recommended for anyone looking to boost their math skills!
Top Tutor
Uttam Nagar, Delhi
9 yrs of
Exp
3 students
132 hrs of classes completed
1000
per hour
Online Classes
Student's Home
Tutor's home
Efficient professional with 9+ years of experience and proven knowledge of lectures, training and development, and adaptive teaching methods. I aim to leverage my skills to successfully fill the significant role of a teacher in your life. Also, through my experience, I have developed interactive teaching methods that can help you understand every concept's very applicability, enabling you to correlate the readings with practical situations.
The lesson was highly participatory, and the subjects were clearly explained with suitable examples. Sir was very clear in his explanations.
Top Tutor
Sector 9, Faridabad
8 yrs of
Exp
6 students
1270 hrs of classes completed
250
per hour
Online Classes
Tutor's home
XI standard students required basic teaching as well as preparing them to get ready for boards in future . Their curiosity for new subjects needs to be given right direction. Their knowledge as well as concepts needs to be enhanced at every step. By joining my classes they will be well prepared for their board class.
My experience in Ms Sanya's tution was very good. The concepts were taught very well. The doubts were cleared easily. The speed of teaching was perfect. Increased my grades compared to my grades before joining this tution. A very comfortable relationship with the teacher. Would like to conclude by thanking Ms Sanya for her wonderful efforts.
Super Tutor
Pandri, Raipur
4 yrs of
Exp
45 students
3230 hrs of classes completed
520
per hour
Online Classes
Hello, my name is Atulya Kumar. I have completed my engineering from IIT (ISM), Dhanbad and am currently pursuing a PhD in Civil Engineering at IIT (ISM), Dhanbad. Teaching physics has been both a passion and a purpose since 2019, and over the years, I have mentored Class XI and XII students, particularly those preparing for JEE Main, JEE Advanced, NEET, and board examinations. I specialize in teaching Class 12 and 11 Physics in a result-oriented and concept-focused manner. My classes are tailored to bridge the gap between theory and application, ensuring students not only understand the fundamentals but can also apply them effectively in competitive exams. In recent years, my students have consistently performed exceptionally well. For example, in NEET 2025, two of my students scored 653 and 639, while many achieved more than 99 percentile in JEE Main 2025. In earlier years, students under my guidance secured AIR 2513 in NEET 2022 and AIR 1702 in NEET 2023, with many crossing the 98th percentile in JEE Main 2023. I adopt a structured approach, focusing on topic-wise concept clarity, MCQ drills, PYQ (previous year questions) practice, and mock test simulations. My JEE sessions emphasize critical topics such as modern physics, electromagnetism, kinematics, and thermodynamics, while NEET classes are tailored toward speed, accuracy, and NCERT alignment. I also give equal importance to board exam preparation, guiding students to score above 90% in Physics through clear explanations, derivation practice, answer writing techniques, and mock board tests. Teaching physics is a personal challenge and joy for me. I strive to build a learning environment where students feel confident, curious, and capable. It’s deeply fulfilling to watch them grow from conceptual struggles to academic excellence, and I remain committed to their success—both in exams and in life.
Knowledgeable tutor. Good hold on physics; all topics covered. My daughter is preparing for NEET exams and is studying physics from Atulya G.
Other Subjects in CBSE - Class 11
Download free CBSE - Class 11 Physics Mechanical Properties of Fluids EXERCISES worksheets
Download Now
