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AAI ATC Physics — Gravitation Important Notes

1. What is Gravitation?

It’s the force of attraction between any two objects in the universe due to their masses.

Universal force — acts whether you like it or not.


2. Important AAI ATC Focused Concepts

3. Newton’s Law of Universal Gravitation

The force of attraction between two masses is proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

\( F = G \frac{m_1 m_2}{r^2} \)

Where:

  • F: Gravitational force (N)
  • G: Universal gravitational constant (6.67 × 10⁻¹¹ Nm²/kg²)
  • m₁, m₂: Masses (kg)
  • r: Distance between centers (m)

4. Acceleration Due to Gravity (g)

The acceleration experienced by an object due to Earth’s gravitational pull.

\( g = \frac{G M}{R^2} \)

Where:

  • M: Mass of Earth
  • R: Radius of Earth

Value on Earth: 9.8 m/s²

5. Relation of g at Height (h)

Gravitational acceleration decreases as you go higher.

\( g_h = g \left(1 - \frac{2h}{R}\right) \)

Where h is the height above Earth’s surface.

GenZ Example

Your phone on the table is attracted by Earth — that’s gravity. Even your fries have weight.

PYQ Type: Unit of G?

Ans: Nm²/kg² (2021 Shift MCQ)

GenZ Example

When you drop your phone and it falls at 9.8 m/s² — that’s g pulling it down.

PYQ Type: Value of g on Earth?

GenZ Example

Less gravity at airplane altitude than ground.

6. Gravitational Potential Energy

Energy due to the position of an object in a gravitational field.

\( U = -\frac{G m_1 m_2}{r} \)

Negative because force is attractive.

7. Escape Velocity (vₑ)

The minimum speed needed to escape Earth’s gravitational pull.

\( v_e = \sqrt{\frac{2 G M}{R}} \)

For Earth: vₑ ≈ 11.2 km/s

8. AAI ATC PYQ Analysis (2021–2023)

2021 Shift 2: Unit of gravitational constant G (theory MCQ)

2022 Shift 1: Value of g at Earth’s surface

2023 Dec: No direct Q — but fair game for theory filler MCQs

GenZ Example

You need to hit 11.2 km/s to escape Earth’s gravity — like a rocket launch.

PYQ Type: (Occasional MCQ in concept papers)

9. Gravitation Formula Quick Revision Sheet

Formula Meaning
\( F = G \frac{m_1 m_2}{r^2} \) Universal Gravitational Force
\( g = \frac{G M}{R^2} \) Acceleration due to gravity
\( g_h = g \left(1 - \frac{2h}{R}\right) \) g at height
\( U = -\frac{G m_1 m_2}{r} \) Gravitational potential energy
\( v_e = \sqrt{\frac{2 G M}{R}} \) Escape velocity

10. Quick Concept Recap

Concept GenZ Example
Gravity attracts all masses Earth pulling your sneakers
g value decreases with altitude You weigh a fraction less on an airplane
Escape velocity How fast a rocket must go to ditch gravity
Negative Potential Energy You always get pulled back by gravity

11. Final AAI ATC Takeaway

Focus Areas:

  • At least 1–2 MCQs per year (theory or unit-based)
  • Unit of G
  • Value of g
  • Universal Law formula
  • Escape velocity definition & formula