Gravitation — Class 9 Physical Science
1. The Universal Law of Gravitation
Every particle in the universe attracts every OTHER particle with a force DIRECTLY proportional to the product of their masses and INVERSELY proportional to the SQUARE of the distance between them.
F = G × (m₁ × m₂) / r², where G = 6.674 × 10⁻¹¹ N m²/kg² (Universal Gravitational Constant).
'Newton's genius was realising that the SAME force that makes an apple fall also keeps the Moon in orbit around the Earth. The force is UNIVERSAL — it acts between ALL objects with mass.'
Key Features of Gravitational Force
- Always ATTRACTIVE (never repulsive).
- Acts along the LINE joining the centres of the two masses.
- Obeys Newton's Third Law: F₁₂ = F₂₁ (equal and opposite).
- Very WEAK for small masses (G is tiny: 10⁻¹¹), but DOMINANT for planetary masses.
- Independent of the MEDIUM between the objects.
Worked Example
Calculate the gravitational force between two 1 kg masses placed 1 m apart. F = (6.67×10⁻¹¹)(1)(1)/(1)² = 6.67×10⁻¹¹ N. 'This force is EXTREMELY small — about the weight of a grain of sand. That's why we don't feel gravitational attraction between everyday objects.'
2. Acceleration Due to Gravity (g)
When an object falls toward Earth, the gravitational force causes an acceleration: g = GM/R², where M = Earth's mass (6×10²⁴ kg), R = Earth's radius (6.4×10⁶ m). g ≈ 9.8 m/s² (or ~10 m/s² for rough calculations).
On Earth's surface: All objects, regardless of mass, fall with the SAME acceleration g (in vacuum). 'A feather and a hammer dropped on the Moon (no air resistance) hit the ground SIMULTANEOUSLY — as demonstrated by Apollo 15 astronauts.'
Variation of g
- With altitude: g DECREASES as height increases. g' = g(R/(R+h))².
- With depth: g DECREASES as you go deeper into Earth.
- At poles vs equator: g is MAXIMUM at poles and MINIMUM at equator (Earth bulges at equator — larger R → smaller g).
3. Equations of Motion Under Gravity (Free Fall)
Replace 'a' with 'g' (taking downward direction as positive, or use g = +9.8 m/s² for downward motion and g = −9.8 m/s² for upward).
v = u + gt. h = ut + ½gt². v² = u² + 2gh.
Worked Examples
Example 1 — Drop: A ball is dropped from height 20 m. Find time to reach ground and speed on impact. u=0, h=20, g=10. h = ½gt² → 20 = 5t² → t = 2s. v = gt = 10×2 = 20 m/s.
Example 2 — Throw Up: Ball thrown up at 30 m/s. Find max height and time to return. At max height, v=0. v² = u² − 2gh. 0 = 900 − 20h → h = 45 m. Time up: v = u − gt → 0 = 30 − 10t → t = 3s. Total time = 6s (symmetry — time up = time down).
Example 3 — Tower: A ball is thrown upward at 20 m/s from a tower 60 m high. When does it hit the ground? Use h = ut − ½gt². −60 = 20t − 5t² → 5t² − 20t − 60 = 0 → t² − 4t − 12 = 0 → (t−6)(t+2) = 0 → t = 6s. 'The negative root (t=−2) has no physical meaning — we take t=6s.'
4. Mass vs Weight
| Property | Mass | Weight |
|---|---|---|
| Definition | Amount of MATTER in a body | GRAVITATIONAL FORCE on the body |
| SI Unit | kilogram (kg) | newton (N) |
| Constant? | SAME everywhere | VARIES — depends on g |
| Measured by | Beam balance | Spring balance |
| Zero possible? | NEVER zero | Weightless when g=0 (deep space) |
| Vector/Scalar | Scalar | Vector (force — has direction) |
'On the Moon (g ≈ 1.6 m/s² ≈ g_earth/6), your MASS is the same, but your WEIGHT is ONE-SIXTH of your Earth weight.'
5. Thrust and Pressure
Thrust: Force acting PERPENDICULAR to a surface (N). Pressure: Thrust per unit AREA. P = F/A (N/m² = Pascal, Pa).
Why Pressure Matters
Same force, SMALLER area → HIGHER pressure. A sharp knife cuts (small edge area → high pressure). Shoulder straps on school bags are WIDE (large area → low pressure on shoulder). Camel feet are broad — they don't sink in sand (low pressure).
6. Buoyancy and Archimedes' Principle
Buoyancy: The UPWARD force exerted by a fluid on an object immersed in it. Buoyant force = weight of fluid DISPLACED = V_immersed × ρ_fluid × g.
Archimedes' Principle: When a body is wholly or partially immersed in a fluid, it experiences an UPWARD force (buoyant force) EQUAL to the WEIGHT of the FLUID DISPLACED by it.
Why Objects Float or Sink
- Object's density < fluid density → FLOATS (buoyant force > weight)
- Object's density = fluid density → NEITHER floats nor sinks (neutral buoyancy)
- Object's density > fluid density → SINKS (weight > buoyant force)
Example: Ice floats on water because density of ice (0.92 g/cm³) < density of water (1 g/cm³). Iron nail sinks in water (7.8 > 1) but floats on mercury (7.8 < 13.6).
7. Relative Density (Specific Gravity)
Relative Density = Density of substance / Density of water at 4°C. Dimensionless (no units). Density of water = 1000 kg/m³ = 1 g/cm³.
8. Common Mistakes
- Confusing mass and weight: 'My weight is 50 kg' — INCORRECT. Weight is 500 N (50 kg × 10 m/s²). The 50 kg is your MASS.
- G ≠ g: G is the universal constant (6.67×10⁻¹¹). g is acceleration due to gravity at Earth's surface (~9.8 m/s²). They are completely different quantities.
- 'Heavier objects fall faster': In VACUUM, all objects fall at the same rate. In air, lighter/larger objects experience more air resistance relative to weight.
- Buoyancy depends on weight of object: It depends on weight of FLUID DISPLACED, not the object.
9. AP Exam Focus
| Topic | Marks |
|---|---|
| Universal law of gravitation | 3-4 |
| Free fall problems (g=10) | 4-5 |
| Mass vs Weight | 2-3 |
| Thrust and Pressure | 2-3 |
| Archimedes' principle and applications | 4-5 |
Quick Self-Test
- g at Earth's surface? (Answer: ~9.8 m/s².)
- A ball thrown up at 40 m/s. Max height? (Answer: u²/2g = 1600/20 = 80 m.)
- Why does a ship float but a small iron nail sinks? (Answer: Ship displaces large volume of water (buoyant force = weight). Nail displaces very little water (buoyant force < weight).)
- Mass of object = 10 kg. Weight on Earth? On Moon? (Answer: 100 N (Earth), ~16.7 N (Moon).)
- Pressure exerted by 100 N force on area 0.5 m²? (Answer: P = 100/0.5 = 200 Pa.)
