Chapter 7 · Class 11-12 & JEE/NEET
Dual Nature of Matter & Radiation
34 topics in 6 parts
Einstein photoelectric equation Photon energy Photon momentum Number of photons Photon flux Radiation pressure on absorber
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 34 topics in Dual Nature of Matter & Radiation
Quantum Theory of Light
- Force Exerted by a Light Beam on a Surface
- Intensity of Light Due to a Light Source
- Photon Density in a Light Beam
- Photon Flux
- Photons Counts Emitted by a Source Per Second
- Properties of Photons
- Photon Energy & Momentum
- Intensity & Distance Relation
- Quantum Efficiency
Radiation Pressure/Force
- Radiation Pressure on Reflecting & Absorbing Surfaces
- Force on Normal & Oblique Surface
- Radiation Force & Momentum Transfer
Photoelectric Effect
- Einstein's Photoelectric Effect
- Failure of Classical Wave Theory of Light to Explain the Laws of Photoelectric Effect
- Laws of Photoelectric Effect
- Study of Photoelectric Effect
- Work Function & Threshold Frequency
- Threshold Wavelength
- Stopping Potential & Maximum Kinetic Energy
- Photocurrent & Saturation Current
- Photoelectric Graphs & Spectral Variation
- Effect of Magnetic & Electric Fields
Photoelectric Cell
- Application of Photoelectric Cell
- Spectral Sensitivity & Photoelectric Yield
Matter Waves
- Application of de Broglie Wave Hypothesis
- Properties of Matter Waves
- de Broglie Wavelength of Particles
- de Broglie Wavelength in Bohr Orbits
- Wave-Particle Duality
- Davisson-Germer Experiment & Electron Diffraction
- Heisenberg Uncertainty Principle
X-Rays
- Production & Coolidge Tube
- Continuous & Characteristic Spectrum
- Minimum Cut-off Wavelength