Gravitation – Simple Study Notes for D.Pharm Physics
1. What is Gravitation?
- Gravitation is a force that pulls two objects with mass toward each other.
- Think of it as an invisible hand that keeps a ball on the ground and pulls the Earth toward the Sun.
2. Everyday Analogy
- Apple on a Tree:
- The apple wants to go down because the Earth pulls it.
- The Earth’s pull is the same force that keeps you on the floor.
3. Key Concepts
| Concept | Simple Explanation | Tiny Example |
|---|---|---|
| Mass | How much “stuff” an object has. | A 10‑kg bag of rice. |
| Weight | How heavy something feels because of gravity. | The bag of rice feels 98 N on Earth. |
| Gravitational Force (F) | The pull between two masses. | 10 kg × 9.8 m/s² = 98 N. |
| Acceleration due to Gravity (g) | Speed increase of a falling object, about 9.8 m/s² on Earth. | A dropped ball speeds up by ~9.8 m every second. |
| Gravitational Field (g) | How strong gravity is at a point. | Same 9.8 m/s² everywhere near Earth’s surface. |
4. Newton’s Law of Universal Gravitation
- Formula:
[ F = G \frac{m_1 m_2}{r^2} ] - What it says:
- The force between two masses is proportional to each mass.
- It gets weaker the farther apart the masses are (square of the distance).
- G is a tiny constant that makes the numbers work.
- Example:
- Mass of Earth ≈ (6×10^{24}) kg.
- Mass of a 1‑kg book = 1 kg.
- Distance ≈ radius of Earth ≈ (6.4×10^6) m.
- Plugging in gives a force of about (6×10^{22}) N – huge, but we feel only the result on the surface.
5. Gravity Near the Earth’s Surface
| Quantity | Symbol | Value | Meaning |
|---|---|---|---|
| Acceleration due to gravity | (g) | 9.8 m/s² | How fast a free‑falling object speeds up. |
| Weight of 1 kg mass | (W) | 9.8 N | The force we feel. |
| Weight of 100 kg mass | (W) | 980 N | The force on a heavy person. |
- Weight = mass × g
- (W = m \times g)
- Example: 10 kg × 9.8 m/s² = 98 N.
6. Variation with Height
- Formula (approximate):
[ g_h = g_0 \left(\frac{R}{R + h}\right)^2 ]- (g_0) = 9.8 m/s² at sea level.
- (R) = Earth’s radius.
- (h) = height above sea level.
- Result:
- At 10 km altitude, (g) is only about 0.9 m/s² less than at sea level.
- Tiny change for everyday life.
7. Gravitational Field Strength
- Definition: How strong gravity is at a point.
- Units: m/s² (same as acceleration).
- Everywhere near Earth’s surface: ~9.8 m/s².
8. Orbital Motion (Why the Moon stays in space)
- A satellite moves forward fast enough that it keeps falling toward Earth but never hits it.
- Balance: Forward speed ↔ Pull of gravity.
9. Quick Calculations
| Question | What to Find | Simple Formula | Example |
|---|---|---|---|
| Weight of a 5‑kg object | Weight | (W = m \times g) | (5,kg × 9.8,m/s^2 = 49,N) |
| Force between two 2‑kg masses 3 m apart | Gravitational force | (F = G \frac{m_1 m_2}{r^2}) | (F ≈ 2.7 × 10^{-10},N) (tiny) |
10. Summary
- Gravitation pulls masses together.
- On Earth, it gives us a constant pull of 9.8 m/s².
- Weight is mass times this pull.
- Gravity weakens with distance (square law).
- Everyday life sees only the familiar 9.8 m/s², unless we go to space.
11. Practice Question
A 20‑kg medicine box is on a scale. What does the scale read?
- Answer: (20,kg × 9.8,m/s^2 = 196,N).
- The scale shows 196 N (or, if it displays mass, 20 kg).
Happy studying! Remember: gravitation is simply the invisible hand that