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Gravitation

CBSE Class 9 Science • Chapter 9 • Detailed Master Notes

Chapter Overview:

Gravity is the universal force of attraction between all matter. This chapter explains the Universal Law of Gravitation, acceleration due to gravity ($g$), difference between Mass and Weight, and principles of Floatation (Archimedes' Principle).

1. Universal Law of Gravitation

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

$$ F = G \frac{M \times m}{d^2} $$

$F$: Gravitational force.
$G$: Universal Gravitational Constant ($6.673 \times 10^{-11} N m^2 kg^{-2}$).
$M, m$: Masses of objects.
$d$: Distance between centers.

2. Acceleration due to Gravity ($g$)

When an object falls towards the earth under gravitational force alone, it is in Free Fall.

From Second Law: $F = ma = mg$.

From Universal Law: $F = \frac{GMm}{R^2}$ (where $R$ is radius of earth).

Equating both: $mg = \frac{GMm}{R^2} \Rightarrow g = \frac{GM}{R^2}$.

Value of $g \approx 9.8 m/s^2$ on Earth.

Note: $g$ is independent of mass of object ($m$). Feather and stone fall at same rate in vacuum.

3. Mass and Weight

Mass ($m$): Quantity of matter in a body. Measure of Inertia. Constant everywhere. SI unit: kg.
Weight ($W$): Force with which earth attracts an object. $W = m \times g$. Variable (depends on $g$). SI unit: Newton ($N$).
Weight on Moon $\approx 1/6^{th}$ Weight on Earth (since $g_{moon} \approx g_{earth}/6$).

4. Thrust and Pressure

Thrust: Force acting perpendicular to a surface.

Pressure: Thrust per unit Area.

$$ P = \frac{\text{Thrust}}{\text{Area}} $$

SI Unit: Pascal ($Pa$) or $N/m^2$.

Application: Nail has pointed tip (Small area $\rightarrow$ High pressure). Bag straps are wide (Large area $\rightarrow$ Low pressure).

5. Archimedes' Principle

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

Buoyancy: Upward force exerted by fluid.

Laws of Floatation:

Density of Object < Density of Fluid $\rightarrow$ Float.
Density of Object > Density of Fluid $\rightarrow$ Sink.

Practice Zone

Q1: Mass of an object is 10 kg. What is its weight on Earth?

Ans: $W = m \times g = 10 \times 9.8 = 98 N$.

Q2: Why does a block of plastic released under water come up to the surface?

Ans: Because the density of plastic is less than water. The buoyant force exerted by water is greater than the weight of the plastic block.