Find the best tutors and institutes for Class 11 Tuition
Q9.2(a):
Explain why
(a) The angle of contact of mercury with glass is obtuse, while that of water with glass is acute.
Solution :
Theoretical Foundation: The Young-Dupré Equation
The behavior of a liquid meniscus at the interface of a solid surface is governed by the vector balance of three interfacial tensions acting at the line of contact. These tensions are defined as:
- $\gamma_{sl}$: Interfacial tension between the solid and the liquid.
- $\gamma_{sg}$: Interfacial tension between the solid and the gas (air).
- $\gamma_{lg}$: Interfacial tension between the liquid and the gas.
The equilibrium condition for the angle of contact $\theta$ is given by the Young's relation: $\cos \theta = \frac{\gamma_{sg} - \gamma_{sl}}{\gamma_{lg}}$ [Per the principle of static equilibrium of surface tensions].
Step 1: Analyzing Water-Glass Interface (Acute Angle)
In the case of water on glass, the adhesive forces (forces between water molecules and glass molecules) are significantly stronger than the cohesive forces (forces between water molecules themselves).
- Since adhesive forces are dominant, $\gamma_{sg} > \gamma_{sl}$.
- Substituting into the relation: $\cos \theta = \frac{(\text{positive value})}{\gamma_{lg}}$.
- This results in $\cos \theta > 0$, implying that $\theta < 90^\circ$ [Mathematical definition of the first quadrant in trigonometry].
Consequently, the liquid spreads to maximize contact with the solid surface, resulting in a concave meniscus and an acute contact angle.
Step 2: Analyzing Mercury-Glass Interface (Obtuse Angle)
In the case of mercury on glass, the cohesive forces (forces between mercury atoms) are extremely strong compared to the adhesive forces (forces between mercury and glass molecules).
- The liquid minimizes its surface area to minimize potential energy [Per the principle of minimum energy configuration].
- In this system, $\gamma_{sl} > \gamma_{sg}$.
- Substituting into the relation: $\cos \theta = \frac{(\text{negative value})}{\gamma_{lg}}$.
- This results in $\cos \theta < 0$, implying that $90^\circ < \theta < 180^\circ$ [Mathematical definition of the second quadrant in trigonometry].
Consequently, the mercury tends to bead up to minimize surface contact with the glass, resulting in a convex meniscus and an obtuse contact angle.
Visual Representation of Contact Angles
Comparison Table
| Feature | Water-Glass | Mercury-Glass |
|---|---|---|
| Dominant Force | Adhesion | Cohesion |
| Contact Angle | Acute ($\theta < 90^\circ$) | Obtuse ($\theta > 90^\circ$) |
| Meniscus Shape | Concave | Convex |
Final Solution: The angle of contact is determined by the balance of surface tensions ($\gamma_{sg}, \gamma_{sl}, \gamma_{lg}$). For water, adhesive forces exceed cohesive forces ($\gamma_{sg} > \gamma_{sl}$), yielding $\cos \theta > 0$ (acute). For mercury, cohesive forces dominate ($\gamma_{sl} > \gamma_{sg}$), yielding $\cos \theta < 0$ (obtuse).
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(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(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.)
- 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
Jahangirpura, Surat
15 yrs of
Exp
3 students
3777 hrs of classes completed
250
per hour
Online Classes
Hello! I'm Ashish Bhatia, and a passionate educator with over 17 years of teaching experience in Maths and Science. My mission is to make learning engaging, and meaningful so that every student develops strong conceptual understanding along with the confidence to excel in examinations and beyond. Over the years, I have mentored students from diverse academic backgrounds, helping them improve not only their grades but also their analytical thinking, logical reasoning, and problem-solving abilities. My classes are designed to ensure that students truly understand concepts rather than memorize formulas. -------------Recognition & Achievements ---------- My commitment to quality teaching has been recognized by Urban Pro, where I have consistently been honoured as one of the Top 10 Tutors in 2024 and 2025. I have also earned the prestigious Top Tutor badge, reflecting consistently positive feedback from students and parents, strong teaching performance, and a proven track record of delivering excellent learning outcomes. The appreciation I receive from parents and students consistently highlights my ability to simplify difficult concepts, maintain engaging classes, encourage students to ask questions freely, and build their confidence in Mathematics and Science. I also prepare students for: • Board Examinations • School Assessments • MCQ Practice I teach students from: • CBSE • ICSE • Gujarat Board and other State Boards My online classes are attended by students from India as well as families living abroad who are looking for structured, high-quality academic support. --------------My Teaching Methodology ------------ Every class follows a systematic approach that focuses on learning, application, and continuous improvement. Step 1 – Concept Clarity Every topic is explained from the basics using digital whiteboards, visual illustrations, practical examples, and simple language. I ensure students understand the logic behind every concept before moving to problem-solving. Step 2 – Guided Practice Students actively solve problems during the class. Rather than simply providing answers, I encourage them to think critically, apply concepts, and develop independent problem-solving skills while receiving immediate feedback. Step 3 – Assessment & Reinforcement Learning is strengthened through: • Chapter-wise assignments • Regular practice worksheets • Weekly assessments • MCQ tests • Previous-year board questions • Doubt-solving sessions • Revision tests before examinations Regular performance analysis helps identify learning gaps early so that improvement is continuous. ------------Why Students & Parents Choose Me-------------- ✔ More than 17 years of teaching experience ✔ Recognized among Urban Pro's Top 10 Tutors (2024 & 2025) ✔ Urban Pro Super Tutor ✔ Concept-based teaching methodology ✔ Interactive live online classes ✔ Small batches for individual attention ✔ Personalized doubt-solving support ✔ Digital notes and study material ✔ Regular tests and performance tracking ✔ Board exam and competitive exam preparation ✔ Friendly, patient, and motivating teaching style My Teaching Philosophy I believe every student has the ability to excel when taught with the right approach. Success is not achieved through rote learning but through understanding concepts, practicing consistently, and developing confidence. My objective is to create independent learners who enjoy learning and can confidently tackle academic challenges. Book a Free Demo Class A free demo session allows students and parents to experience my teaching methodology before enrolling. During the demo session, I will: • Assess the student's current academic level. • Teach a topic through an interactive live class. • Identify conceptual strengths and learning gaps. • Suggest a personalized learning plan based on the student's goals. Whether your child needs help strengthening fundamentals, improving school performance, preparing for board examinations, or building confidence in Mathematics and Science, I am committed to providing structured, result-oriented, and engaging online learning. Let's build strong concepts today for a brighter academic future tomorrow. WHAT PARENTS & STUDENTS SAY ---------- Nothing reflects a teacher's impact better than the words of students and parents. Here's what some of them have shared about their learning experience with me on UrbanPro: "The teaching methodology is excellent. He explains the concepts with multiple real and live examples. My son liked his teaching very much." — Parent of a CBSE Class 7 student "The classes have been superb. Topics are being made easy to understand, maths is fun to study now. No matter how difficult the topic, Sir makes sure to make it simple and easy to understand." — CBSE Class 12 student "Ashish is an outstanding online Maths tutor. His teaching style is clear, patient and engaging. My child's grades and understanding of Mathematics have improved significantly." — Parent of a Class 8 student "He is very dedicated. My daughter is now able to understand the concepts easily." — Parent of a CBSE Class 10 student "Ashish Sir is very dedicated and always on time. He makes my son practice more problems during class. My son is now in the top five in his class." — Parent of a CBSE Class 11 student These reviews consistently highlight the qualities I strive to bring into every class—concept clarity, patience, interactive teaching, structured practice, and a genuine commitment to helping every student achieve their best academically.
Ashish Bhatia is very dedicated and always on time. He makes my son practice more problems during class, and because of this we have seen a lot of improvement in his performance. My son is now in the top five in his class.
Top Tutor
Peera Garhi, Delhi
8 yrs of
Exp
2 students
72 hrs of classes completed
700
per hour
Online Classes
Student's Home
Tutor's home
I am having more than 8+ years of experience to teach the Computer Science/ informatic Practice subject to the students of 11th class. I can teach all boards students.
Top Tutor
Vile Parle East, Mumbai
10 yrs of
Exp
5 students
201 hrs of classes completed
500
per hour
Online Classes
Tutor's home
Chemistry class 11 and cbse and state board free lance tutor online as well as teaching at my home
She was very good in explaining my 11th grade basics are strong because of her. She was very supportive and understanding.
Top Tutor
Kukatpally, Hyderabad
10 yrs of
Exp
1 student
4 hrs of classes completed
1000
per hour
Online Classes
I specialize in teaching Chemistry to students in Classes 11 and 12, with a strong focus on competitive exam preparation for IIT JEE and NEET. With 10 years of teaching experience, I have developed a deep understanding of the exam patterns, question types, and techniques needed to succeed in these rigorous entrance tests. My goal is to simplify complex chemical concepts and guide students toward achieving top scores. I hold a Master of Science (M.Sc.) degree in Chemistry, which has equipped me with a strong academic foundation to teach both theoretical and application-based chemistry. I emphasize not just rote learning but deep understanding, so students can apply their knowledge across multiple question formats and problem types in both school and competitive exams. I’ve also cleared several national-level exams myself, including GATE, BARC, and TIFR. These personal academic accomplishments demonstrate not only my subject expertise but also my firsthand experience of the competitive exam landscape. This allows me to offer students insights into how to approach exam strategy, manage time effectively, and stay motivated throughout their preparation journey. I primarily conduct online classes and make full use of digital tools to enhance the learning experience. I use a smart whiteboard for explanations and problem-solving sessions, and my classes are highly interactive. I follow a clear lesson plan and make practice a central part of my teaching approach. Regular doubt-clearing sessions, mock tests, and revision marathons ensure that students stay on track and build confidence in their preparation. Students receive curated notes, study materials, and a variety of question sets to strengthen their grasp on each topic. I also provide tips for solving questions faster and help students analyze their performance in tests to identify areas of improvement. Teaching Chemistry is more than just a profession for me—it’s a passion. I am deeply committed to each student’s success and take pride in seeing them grow not only in their academic performance but also in their overall confidence. If you're aiming to crack competitive exams or simply improve your Chemistry skills, I am here to guide you every step of the way.
My Class 11 Chemistry teacher is truly exceptional. She explains every concept in a simple, clear, and engaging way, making even difficult topics easy to understand. Her teaching style is well-organized, and she always encourages students to ask questions without hesitation. She is patient, supportive, and genuinely cares about her students' learning and success. Her regular practice sessions, real-life examples, and helpful guidance have made Chemistry much more interesting and enjoyable for me. I highly recommend her to any student who wants to build a strong foundation in Chemistry. Thank you for your dedication, hard work, and inspiring teaching.
Top Tutor
Bhestan, Surat
5 yrs of
Exp
2 students
1148 hrs of classes completed
500
per hour
Online Classes
I have over 5 years of experience teaching Class 11 CBSE students in Physics, Chemistry, and Mathematics, following the latest CBSE and NCERT curriculum and examination pattern. My teaching approach focuses on building strong conceptual foundations while developing problem-solving skills required for board examinations and competitive-level questions. I explain every topic in a structured and student-friendly manner, starting from basic concepts and gradually moving towards application-based and higher-order questions. Special emphasis is given to NCERT theory, important derivations, numerical problems, diagrams, formulas, reactions, and previous-year examination patterns. Over the years, I have helped many Class 12 students improve their academic performance, with several students scoring 90% and above in their board examinations. I regularly identify individual learning gaps and provide targeted practice, revision, doubt-solving, and exam-oriented guidance. My goal is not only to help students score high marks but also to make Physics, Chemistry, and Mathematics clear, logical, and easy to understand through consistent practice and personalized guidance.
As a parent of an 11th-grade student, I am very happy with the teaching provided by Shivam Sir. He teaches every topic in a simple, clear, and easy-to-understand way, making even difficult concepts much easier for my son to grasp. His classes are interactive, well-structured, and focused on building strong conceptual understanding rather than just memorization. I have noticed a significant improvement in my son's confidence, problem-solving skills, and academic performance since he started learning from Shivam Sir. He is always patient, encourages students to ask questions, and ensures that every doubt is cleared before moving ahead.
Other Subjects in CBSE - Class 11
Download free CBSE - Class 11 Physics Mechanical Properties of Fluids EXERCISES worksheets
Download Now
