Board exam focus — Gravitation (CBSE & HBSE)

CBSE emphasises the universal law of gravitation, deriving and using g, distinguishing mass from weight, and the full fluid sub-topic (thrust, pressure, buoyancy, Archimedes' principle and relative density) with numericals. HBSE follows the same NCERT content but tends to ask more definition-based and direct-substitution questions, especially on weight on the moon (1/6th), Archimedes' principle and relative density calculations.

Universal Law of Gravitation, Free Fall and g

Universal Law of Gravitation (Newton)

Every object in the universe attracts every other object with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres.

$$F = \frac{G \, m_1 m_2}{d^2}$$

• m₁, m₂ = masses of the two objects, d = distance between their centres.
• G = universal gravitational constant = 6.67 × 10⁻¹¹ N·m²/kg² (same everywhere in the universe).
• The force is mutual (action-reaction pair) and acts along the line joining the centres.
• It is an inverse-square law: if distance doubles, force becomes one-fourth.

Trap: G (capital, universal constant) is NOT the same as g (acceleration due to gravity). G is constant everywhere; g changes with location.

Importance of the Universal Law

It explains the force that binds us to the Earth, the motion of the Moon around the Earth, the motion of planets around the Sun, and the tides caused by the Moon and Sun.

Free Fall and Acceleration due to Gravity (g)

When an object falls towards the Earth under gravity alone, it is in free fall, and it accelerates. This acceleration is g (acceleration due to gravity).

From F = ma and F = GMm/R², for a body of mass m near Earth's surface:

$$g = \frac{G M}{R^2}$$

where M = mass of Earth, R = radius of Earth.

• g does not depend on the mass of the falling body — all bodies fall with the same g (a feather and a stone fall together in vacuum).
• Standard value: g = 9.8 m/s² (often taken as 9.8 or sometimes 10 m/s² in problems).
• g is slightly greater at the poles (R smaller) and smaller at the equator (R larger), and decreases with altitude and depth.

Equations of Motion under Gravity

Replace a with g and s with height h. Taking downward as positive:

1. v = u + gt
2. h = ut + ½gt²
3. v² = u² + 2gh

For an object dropped from rest, u = 0. For an object thrown upward, g is negative (retardation) and at the highest point v = 0.

Mass vs Weight and Weight on the Moon

Mass

Mass is the amount of matter contained in a body.

• It is a scalar quantity and remains constant everywhere (Earth, Moon, space).
• SI unit: kilogram (kg).
• Mass is a measure of inertia.

Weight

Weight is the force with which the Earth (or any celestial body) attracts an object towards its centre.

$$W = m \times g$$

• It is a vector (force), directed towards the centre of the Earth.
• SI unit: newton (N).
• Weight changes from place to place because g changes (with location, altitude, and the celestial body).

Mass vs Weight

Weight of an Object on the Moon

The Moon's mass and radius are smaller than the Earth's, so its gravitational acceleration is about one-sixth that of the Earth.

$$W_{moon} = \frac{1}{6} \, W_{earth}$$

• The mass of the object stays the same on the Moon.
• Only the weight becomes 1/6th because g(moon) ≈ (1/6) g(earth).

Trap: A common mistake is saying mass changes on the Moon. Mass is constant; only weight changes because g changes. Use W = mg and g(moon) = g(earth)/6.

Thrust, Pressure, Buoyancy, Archimedes' Principle and Relative Density

Thrust and Pressure

• Thrust is the force acting on a surface in a direction perpendicular (normal) to the surface. SI unit: newton (N).
• Pressure is the thrust per unit area.

$$P = \frac{\text{Thrust (Force)}}{\text{Area}} = \frac{F}{A}$$

• SI unit of pressure: pascal (Pa), where 1 Pa = 1 N/m².
• For the same force, smaller area gives larger pressure (sharp knives, pointed nails); larger area gives smaller pressure (camel's broad feet, wide foundations, school bag straps).

Pressure in Fluids and Buoyancy

• Fluids (liquids and gases) exert pressure in all directions, including on the walls and base of the container.
• When a body is immersed in a fluid, the fluid exerts an upward force on it called the buoyant force (upthrust). This tendency is called buoyancy.
• The buoyant force depends on the density of the fluid and the volume of the body submerged.
• An object floats if its density is less than that of the fluid, and sinks if its density is greater than that of the fluid.

Archimedes' Principle

When a body is immersed fully or partially in a fluid, it experiences an upward (buoyant) force equal to the weight of the fluid displaced by it.

Applications: design of ships and submarines, lactometers (to test milk purity), and hydrometers (to measure liquid density).

Density and Relative Density

• Density = mass per unit volume.

$$\text{Density} = \frac{\text{Mass}}{\text{Volume}}$$

SI unit: kg/m³ (also g/cm³).

• Relative density (R.D.) is the ratio of the density of a substance to the density of water.

$$\text{R.D.} = \frac{\text{Density of substance}}{\text{Density of water}}$$

• Relative density has no unit (it is a ratio).
• Density of water = 1000 kg/m³ = 1 g/cm³.
• If R.D. > 1, the substance sinks in water; if R.D. < 1, it floats.

Tip: Apparent loss in weight of a body in a fluid = weight in air − weight in fluid = buoyant force = weight of fluid displaced. This is the practical form of Archimedes' principle used in numericals.

Frequently asked questions

Are these Gravitation notes free?

Yes — the Gravitation notes for Science (Class 9) on Siksha Sarovar are completely free to read, with no account required.

Do these notes follow CBSE and HBSE?

Yes. The Gravitation notes are NCERT-aligned and include guidance for both CBSE and Haryana Board (HBSE), with important questions and MCQs for revision.

What does the Gravitation chapter cover?

Concept explanations, key formulas and definitions, fully solved examples and board-pattern practice questions for Gravitation.