Chapter 18 · Class 11-12 & JEE/NEET
Nuclear Physics
32 topics in 11 parts
Nuclear radius Nuclear density Nuclear mass defect Mass defect using atomic masses Nuclear binding energy Binding energy per nucleon
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 32 topics in Nuclear Physics
Nuclear Structure
- Composition & Nuclide Notation
- Nuclear Size & Density
- Nuclear Forces
- Nuclear Stability & Neutron-Proton Ratio
Mass-Energy Equivalence
- Mass-Energy Equivalence
Nuclear Binding Energy
- Mass Defect
- Binding Energy Per Nucleon
- Binding Energy Curve
- Separation Energy
Radioactivity
- Alpha Decay
- Beta Decay & Electron Capture
- Gamma Decay
- Nuclear Radiation Properties
Radioactive Decay Law
- Decay Constant & Activity
- Half-Life
- Mean Life
- Measurement of Radioactivity
Radioactive Series & Equilibrium
- Radioactive Decay Series
- Parent-Daughter Growth & Accumulation
- Radioactive Equilibrium
- Competing Decay Modes
- Multi-Nuclide Decay
Radioactive Dating & Applications
- Radioactive Dating
- Radioisotope Applications
Nuclear Reactions
- Conservation Laws & Reaction Identification
- Q-Value & Threshold Energy
- Reaction Kinematics
Nuclear Fission
- Energy Release & Chain Reactions
Nuclear Reactors
- Neutron Capture, Leakage & Moderation
- Reactor Power & Energy
Nuclear Fusion
- Thermonuclear Fusion
- Fusion in the Sun