Gravitation – Study module with Revision Notes

Study Module & Revision Notes — Gravitation (NCERT-aligned)

Overview: Gravitation is a universal attractive force that acts between every pair of masses. In this chapter we study Newton’s Universal Law of Gravitation, the acceleration due to gravity near Earth’s surface, variation of gravity with distance, the motion of freely falling bodies, and the physics behind satellites and orbital motion. These notes are designed to match the NCERT textbook level and to help you prepare for CBSE Class 9 examinations.

1. Universal Law of Gravitation

Newton’s Universal Law of Gravitation states: Every point mass attracts every other point mass with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

Where: F = magnitude of gravitational force, m₁ and m₂ = masses, r = distance between their centres, and G = gravitational constant ≈ 6.67 × 10⁻¹¹ N·m²/kg².

Direction: The force acts along the line joining the centres and is attractive.

2. Gravitational Field & Acceleration due to Gravity

The gravitational field (or intensity) at a point is defined as the force per unit mass experienced by a small test mass placed at that point.

For Earth, taking M as Earth's mass and R as Earth's radius, acceleration due to gravity at Earth's surface is g = GM / R². Numerically, g ≈ 9.8 m/s² (commonly approximated as 9.8 or 10 m/s² depending on the problem).

3. Variation of g with Altitude and Depth

With altitude: At height h above the surface, g becomes

With depth: At a depth d below the surface (inside Earth, assuming uniform density),

Important: For CBSE-level problems, use the approximations & remember to state assumptions (e.g., Earth as a sphere of uniform density where required).

4. Mass and Weight — Key Differences

Mass is the amount of matter in a body (in kg), a scalar and invariant. Weight is the gravitational force acting on the mass: W = m g. Weight depends on the value of g and thus on location (height/depth), whereas mass does not.

5. Free Fall and Equations of Motion

A body falling under gravity with negligible air resistance is in free fall — acceleration is g directed downward. Use standard kinematic equations with acceleration = g:

For objects dropped from rest: u = 0, so s = ½ g t² and v = g t.

6. Apparent Weight & Weightlessness

If a body is in an accelerating elevator or a non-inertial frame, its apparent weight changes. Apparent weight = normal reaction = m(g ± a) depending on direction of acceleration. If in free fall (e.g., orbiting spacecraft), apparent weight is zero — called weightlessness — because both you and the spacecraft accelerate at the same rate under gravity.

7. Motion of Planets, Satellites and Orbital Motion

For a satellite (or object) moving in a circular orbit of radius r around Earth, the centripetal force required is provided by gravitational attraction:

Orbital period T for a circular orbit is

Escape velocity: Minimum speed to escape Earth’s gravity (ignoring atmosphere):

Numerical value from Earth: ≈ 11.2 km/s.

8. Kepler’s Laws — Brief Mention

Although Kepler’s three laws are treated more in higher classes, it's useful to remember the basic ideas: planetary orbits are elliptical (Kepler I), equal areas are swept in equal times (Kepler II), and orbital period squared is proportional to the cube of the semi-major axis (Kepler III). For circular orbits, Kepler III leads to T² ∝ r³, consistent with the formula above.

9. Important Formula Sheet (Quick Reference)

10. Solved Short Numericals (CBSE-style)

11. Common Question Types & Exam Strategy

1. Short answer: Definitions — law of gravitation, gravitational field, weightlessness. Keep answers precise and include formula where applicable.
2. Numerical problems: Practice kinematics under constant g and gravitation-based force problems (two mass system, variation of g with height/depth).
3. Long answer / application: Explain difference between mass and weight with examples (Moon, Earth, in elevator). Draw diagrams for satellites and circular motion when asked.
4. Diagrams: Centre-of-mass line of action, free body diagrams for weights, orbit sketch for satellites — neat diagrams fetch marks.

12. Quick Revision Checklist (Before the Exam)

• Memorise key formulae and the value of G.
• Understand vector direction of gravitational force between two masses.
• Practice at least 8–10 numerical problems: free fall, variation of g, orbital velocity, escape velocity.
• Revise concept questions: weightlessness, apparent weight, and difference between mass & weight.
• Time yourself while solving numericals — accuracy beats speed in board exams.