NCERT Solutions for Class 11 Physics Chapter 10 – Mechanical Properties of Fluids
Chapter 10 of Class 11 Physics, Mechanical Properties of Fluids, explores the behaviour of liquids and gases under rest and motion. Fluids (liquids and gases) differ from solids in their ability to flow and take the shape of their container. This chapter covers both fluid statics — study of fluids at rest, including pressure, Pascal's Law, buoyancy, and Archimedes' Principle — and fluid dynamics — study of fluids in motion, through the equation of continuity and Bernoulli's theorem. Bernoulli's Principle is one of the most important and widely applied concepts in Physics, explaining the lift on aircraft wings, the working of spray guns, and the Venturi meter. Students also study viscosity, which measures a fluid's internal resistance to flow, and Stokes' Law for the terminal velocity of spheres falling through viscous media. The chapter concludes with surface tension — a surface property arising from cohesive forces — explaining capillarity, the shape of liquid drops, and the working of detergents. This chapter has direct applications in aeronautics, hydraulics, blood flow in arteries, and daily phenomena. NCERT solutions for Chapter 10 present detailed, exam-ready answers to all exercises under the latest CBSE syllabus.
NCERT Solutions PDF – Class 11 Physics Chapter 10 (All Exercises)
| Resource Name | Description | Best For |
|---|---|---|
| NCERT Solutions | Detailed answers and explanations for NCERT textbook questions across all classes and subjects. | Homework, assignments, and exam preparation |
| NCERT Solutions for Class 11 | Chapter-wise solutions for all Class 11 subjects including Physics, Chemistry, Mathematics, Biology, and English. | Class 11 board exam preparation |
| NCERT Solutions for Class 11 Physics | Step-by-step solutions covering all chapters such as Motion, Laws of Motion, Work Energy and Power, Thermodynamics, and Waves. | Concept building and numerical problem-solving |
| NCERT Exemplar Class 11 Physics | Advanced and application-based questions designed to strengthen conceptual understanding and analytical skills. | JEE, NEET, Olympiads, and higher-order practice |
| Physics Formula | Chapter-wise collection of important formulas, equations, and derivations for quick revision. | Last-minute revision and numerical practice |
Important Formulas – Chapter 10: Mechanical Properties of Fluids
| Formula | Expression | Description |
|---|---|---|
| Fluid Pressure | P = F / A | Pressure = force per unit area; unit: Pascal (Pa) |
| Pressure at depth h | P = P₀ + ρgh | P₀ = atmospheric pressure; ρ = fluid density |
| Pascal's Law | ΔP transmitted equally | Pressure change in enclosed fluid is transmitted uniformly |
| Archimedes' Principle | F_b = ρ_fluid · V_sub · g | Buoyant force = weight of displaced fluid |
| Equation of Continuity | A₁v₁ = A₂v₂ | Conservation of mass in steady flow |
| Bernoulli's Equation | P + ½ρv² + ρgh = constant | Conservation of energy in ideal fluid flow |
| Torricelli's Theorem | v = √(2gh) | Speed of efflux from a hole at depth h below free surface |
| Viscous Force (Stokes' Law) | F = 6πηrv | η = viscosity, r = sphere radius, v = velocity |
| Terminal Velocity | v_t = 2r²(ρ−σ)g / 9η | ρ = sphere density, σ = fluid density |
| Reynolds Number | Re = ρvD / η | Re < 1000: laminar; Re > 2000: turbulent |
| Surface Tension | T = F / L | Force per unit length on a liquid surface; unit: N/m |
| Excess Pressure (bubble) | ΔP = 4T/r (soap); 2T/r (liquid drop) | Soap bubble has 2 surfaces; liquid drop has 1 |
| Capillary Rise | h = 2T cosθ / (rρg) | θ = contact angle; r = tube radius |
Subtopics Explained – Chapter 10: Mechanical Properties of Fluids
Fluid Pressure and Pascal's Law
Pressure in a static fluid increases with depth as P = P₀ + ρgh. Pascal's Law states that any pressure applied to an enclosed fluid is transmitted equally and undiminished in all directions. This principle underlies hydraulic lifts, car brakes, and hydraulic presses — all high-value real-life applications in NCERT problems.
Archimedes' Principle and Buoyancy
A body immersed in a fluid experiences an upward buoyant force equal to the weight of the displaced fluid. This explains why ships float, submarines dive, and hot air balloons rise. The condition for floating is that buoyant force ≥ weight of the object.
Bernoulli's Theorem and Applications
For steady, incompressible, non-viscous flow, the sum P + ½ρv² + ρgh remains constant along a streamline. Applications include: lift on aircraft wings (Venturi effect), Pitot tube, spray atomisers, and the Venturi meter. This is one of the most conceptually rich and exam-important topics in the chapter.
Viscosity and Stokes' Law
Viscosity is a measure of a fluid's resistance to flow. Honey is more viscous than water. The viscous drag force on a sphere is given by Stokes' Law: F = 6πηrv. At terminal velocity, this drag force plus buoyancy exactly balances gravity, so the sphere moves at constant speed.
Surface Tension and Capillarity
Surface tension arises from cohesive forces between liquid molecules at the surface. It causes soap bubbles, water droplets, and insects walking on water. Capillary rise (or depression) is observed in narrow tubes — water rises in glass (contact angle < 90°) while mercury is depressed (contact angle > 90°). Detergents work by reducing surface tension.
Quick Reference Table – Important Values and Comparisons
| Concept | Key Detail | Application |
|---|---|---|
| Atmospheric Pressure | 1.013 × 10⁵ Pa = 76 cm Hg | Barometer, weather systems |
| Density of water | 1000 kg/m³ at 4°C | Buoyancy calculations |
| Viscosity of water (20°C) | ~1 × 10⁻³ Pa·s | Stokes' Law problems |
| Surface tension of water | 0.073 N/m at 20°C | Capillarity, drops, bubbles |
| Bernoulli vs Torricelli | Torricelli is a special case of Bernoulli | Tank drainage problems |
| Laminar vs Turbulent | Re <1000 → laminar; Re >2000 → turbulent | Pipe flow design |
| Continuity Equation | Av = constant for incompressible flow | Nozzles, arterial blood flow |
| Soap Bubble Pressure | ΔP = 4T/r (two surfaces) | Why smaller bubbles have higher pressure |
NCERT Solutions for Class 11 Physics Chapter 10: Mechanical Properties of Fluids
Fluids possess unique properties such as pressure, density, viscosity, and surface tension. These properties determine how liquids and gases behave under different conditions. The chapter explains fluid motion and the factors affecting fluid behavior. Students learn practical applications involving hydraulic systems, pipelines, and natural phenomena. Understanding fluid properties is essential for solving numerical problems and interpreting real-life examples. This topic also serves as a foundation for advanced studies in fluid mechanics and engineering.
Fluid pressure is the force exerted per unit area by a fluid. According to Pascal’s Law, pressure applied to an enclosed fluid is transmitted equally in all directions. This principle forms the basis of hydraulic machines such as lifts and brakes. The chapter explains pressure variations with depth and the practical significance of pressure transmission. Numerical questions involving pressure calculations frequently appear in examinations. Understanding these concepts helps students relate theoretical principles to engineering applications.
Archimedes’ Principle states that a body immersed in a fluid experiences an upward buoyant force equal to the weight of the displaced fluid. This principle explains why objects float or sink. Students learn how buoyancy affects ships, submarines, and floating devices. Examination questions often involve calculations related to apparent weight and fluid displacement. Understanding Archimedes’ Principle helps students analyze everyday phenomena and solve practical numerical problems effectively.
Viscosity is the internal resistance offered by a fluid to flow. Thick liquids such as honey have higher viscosity than water. The chapter discusses factors affecting viscosity and its role in fluid dynamics. Students learn how viscosity influences movement through fluids and the functioning of lubrication systems. Questions related to fluid flow and resistance often appear in examinations. A clear understanding of viscosity helps explain many industrial and natural processes involving liquids and gases.
Bernoulli’s Principle states that an increase in the speed of a fluid results in a decrease in pressure. This relationship is widely used to explain aircraft lift, atomizers, and fluid flow in pipes. The chapter introduces the Bernoulli equation and its practical applications. Students often encounter conceptual and numerical questions based on this principle. Understanding Bernoulli’s Principle strengthens knowledge of fluid mechanics and demonstrates how physics explains many technological innovations.