Chapter 16 · Class 11-12 & JEE/NEET
Mechanical Properties of Fluids
46 topics in 12 parts
Pressure Mass density Relative density Hydrostatic gauge pressure Absolute pressure in a liquid Pressure difference between levels
Key ideas
4. Systematic Comparison & Parameter Classifications
| Body Shape | Axis of Rotation | Moment of Inertia (I) | Shape Factor (k² / R²) |
|---|---|---|---|
| Thin Ring / Hollow Cylinder | Central Axis Perpendicular to Plane | M R² | 1.0 (Slowest Down Incline) |
| Solid Disc / Solid Cylinder | Central Axis Perpendicular to Plane | (1/2) M R² | 0.50 |
| Solid Sphere | Diameter Axis | (2/5) M R² | 0.40 (Fastest Down Incline) |
| Spherical Shell (Hollow) | Diameter Axis | (2/3) M R² | 0.67 |
| Uniform Rod (Length L) | Through Center Perpendicular to Length | (1/12) M L² | L² / (12 R²) |
Exam Worked Example
Problem: A solid sphere and a solid cylinder of equal mass M and radius R roll down the same inclined plane without slipping from rest. Find the ratio of their accelerations down the incline.
● Step 1: Formula for linear acceleration in pure rolling: a = (g sin θ) / (1 + k²/R²).
● Step 2: For solid sphere, k²/R² = 2/5 = 0.4. Therefore, a_sphere = (g sin θ) / (1 + 2/5) = 5/7 g sin θ ≈ 0.714 g sin θ.
● Step 3: For solid cylinder, k²/R² = 1/2 = 0.5. Therefore, a_cyl = (g sin θ) / (1 + 1/2) = 2/3 g sin θ ≈ 0.667 g sin θ.
● Step 4: Ratio a_sphere / a_cyl = (5/7) / (2/3) = (5 * 3) / (7 * 2) = 15 / 14 ≈ 1.07. The solid sphere reaches the bottom first!
Checkpoint
1. When a ballet dancer pulls her arms inward during a spin on smooth ice, what happens to her kinetic energy?
All 46 topics in Mechanical Properties of Fluids
Hydrostatics
- Measuring Pressure & Manometers
- Pressure Variation with Depth
- Forces on Immersed Surfaces
- Fluid in Accelerating Frame
- Rotating Fluid in Vessel
Pascal's Law
- Hydraulic Lift & Pressure Transmission
- Pressure Diagrams & Boundary Forces
- Equipressure Lines
Buoyancy & Floatation
- Archimedes' Principle
- Calculation of Buoyant Force
- Centre of Buoyancy
- Equilibrium of Floating Bodies
- Buoyant Force in Accelerating Frame
Hydrodynamics
- Streamline & Turbulent Flow
- Types of Fluid Flow
- Principle of Continuity
Bernoulli's Equation
- Energy Associated with Moving Liquid
- Applications & Limitations of Bernoulli's Theorem
- Venturi Meter & Pitot Tube
- Static & Dynamic Pressure
Velocity of Efflux: Torricelli's Theorem
- Torricelli's Law & Efflux Speed
- Horizontal Range of Escaping Liquid
- Force of Reaction & Liquid Jet Thrust
- Time to Empty a Container
Viscosity
- Newton's Law of Viscosity
- Coefficient of Viscosity & Units
- Stoke's Law & Viscous Drag Force
- Effect of Temperature on Viscosity
- Critical Velocity & Poiseuille's Flow
Terminal Velocity
- Terminal Speed of Falling Sphere
- Motion of Spheres & Bubbles in Viscous Medium
Surface Tension
- Causes & Molecular Theory of Surface Tension
- Force of Adhesion & Cohesion
- Measurement of Surface Tension
- Angle of Contact & Meniscus Shape
Surface Energy
- Relation Between Surface Tension and Surface Energy
- Work Done in Expanding Drop & Bubble
- Splitting & Coalescence of Liquid Drops
Excess Pressure Inside a Liquid Drop and a Bubble
- Excess Pressure in Soap Bubble
- Excess Pressure in Air Bubble in Liquid
- Excess Pressure on Curved Surface
- Coalescence of Soap Bubbles
Capillarity
- Wetting and Non-Wetting Liquids
- Capillary Rise & Ascent Formula
- Capillary of Insufficient Length
- Practical Applications of Capillarity