Summary & Quick Quiz ഗുരുത്വാകർഷണം
The whole chapter on one page: the five key boxes, every formula with its unit, the mistakes to avoid, flashcards, a scored quiz and your study checklist.
1. The chapter in one picture
Read it from the middle outwards: one law (F = Gm1m2/d2) explains falling coconuts, weight, weightlessness, the Moon’s orbit and satellites.
2. The key boxes of the textbook
The Earth attracts every object; the direction is towards the centre of the Earth (ഭൂകേന്ദ്രം). This attractive force is the Earth’s gravitational force. – page 5
Every object in the universe attracts every other object. The force is directly proportional to the product of the masses (ഗുണനഫലം) and inversely proportional to the square of the distance (അകലത്തിന്റെ വർഗം) between them. – page 6
The acceleration produced in objects by the Earth’s gravitational force is g. The object’s own mass is not in the formula, so all objects fall together (without air). – page 7
1 kgwt is the force with which the Earth attracts a 1 kg mass. Weight (ഭാരം) is a force, measured in newton with a spring balance. – page 10
A body allowed to fall freely from a height falls only because of the Earth’s gravitational force; such motion is free fall. A body in free fall shows no weight on a balance: weightlessness (ഭാരമില്ലായ്മ). – page 11
In uniform circular motion (സമവർത്തുളചലനം) the speed is constant but the velocity is not – its direction changes. A force towards the centre, the centripetal force, is needed; without it the body flies off along the tangent (തൊടുവര). For satellites, gravity is the centripetal force. – page 11
3. Formulas & units
📐 Formulas & units card
| Quantity | Formula | SI unit | Remember |
|---|---|---|---|
| Gravitational force | F = G m1m2 / d2 | newton (N) | d is the distance between the centres; double d → F becomes ¼ |
| Gravitational constant G | G = 6.67 × 10−11 | N m2/kg2 | the same everywhere in the universe (Cavendish, 1798) |
| Force at a height h | F = GMm / (R + h)2 | N | use R + h, the distance from the Earth’s centre |
| Acceleration due to gravity | g = GM / R2 | m/s2 | 6.67 × 10−11 × 6 × 1024 / (6.4 × 106)2 = 9.77 ≈ 9.8 m/s2 |
| Weight | W = mg | N (also kgwt) | 1 kgwt = 9.8 N; mass in kg never changes |
| Falling from rest (u = 0) | v = gt, h = ½gt2, v2 = 2gh | m/s, m | t = √(2h/g); the mass is not needed |
| Thrown straight up with u | v = u − gt, h = ut − ½gt2, v2 = u2 − 2gh | m/s, m | at the top v = 0: time up = u/g = time down; maximum height = u2/2g |
🌍 Values of g and constants
| Place | g (m/s2) | Why |
|---|---|---|
| Earth (average) | 9.8 | g = GM/R2 with M = 6 × 1024 kg, R = 6.4 × 106 m |
| Poles (ധ്രുവപ്രദേശം) | ≈ 9.83 (greatest) | the Earth is flattened at the poles – smallest distance to the centre |
| Equator (ഭൂമധ്യരേഖാപ്രദേശം) | ≈ 9.78 (least on the surface) | greatest distance to the centre |
| Centre of the Earth | 0 | pulled equally from all sides – the pulls cancel |
| Moon | 1.62 (≈ 1/6 of 9.8) | M = 7.34 × 1022 kg, R = 1.74 × 106 m; 1.62/9.8 = 0.165 |
| Jupiter | 23.1 | a 100 kg object weighs 2310 N there |
- Writing weight in kg. Weight is a force → newton (N). “50 kg” on a spring balance really means 50 kgwt = 490 N.
- Forgetting to square the distance, or using the height above the ground instead of the distance from the centre. For a satellite at height h use (R + h)2.
- “Heavier objects fall faster.” Without air they fall together: g = GM/R2 has no m in it.
- “The heavier body pulls harder.” The force is mutual and equal: the Earth pulls the Moon with F and the Moon pulls the Earth with the same F.
- “There is no gravity in the space station.” At 400 km g is about 8.7 m/s2 (≈ 89 %); the astronauts float because they are in free fall.
- “Mass changes on the Moon.” Only the weight changes (to about 1/6); the mass stays the same.
- Thinking g is a constant like G. g changes from place to place; G is universal.
- Sign errors for upward throws. Take upwards as positive and use −g (v = u − gt), or use “time up = time down”.
- Losing units or powers of ten. 10−11 × 1024 = 1013; (6.4 × 106)2 = 40.96 × 1012. Always end with a unit.
4. Flashcards
Click a card to flip it.
5. Scored quiz
Answer all thirteen, then press Check my answers. Each wrong answer shows the page to revise. Use g = 9.8 m/s2 unless the question says otherwise.
6. Your study checklist
Ticks come from “Mark this page as completed” at the bottom of each page.
Next: the model test paper ▶ – attempt it on paper with a timer first, then check with the solved paper.