🌍 Chapter 1: Gravitation – Class 10 Science (Maharashtra Board)

Gravitation is one of the fundamental forces in nature. It governs the motion of planets, the tides in oceans, and even the way we stay grounded on Earth. In this chapter, we’ll explore the laws of gravitation, motion of objects under gravity, and key concepts like escape velocity, free fall, and more.

🔭 What is Gravitation?

Gravitation is a force of attraction that acts between any two objects in the universe. Every object 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 them.

This universal law of attraction was first formulated by Sir Isaac Newton in the 17th century and is known as the Universal Law of Gravitation.

⚖️ Newton’s Universal Law of Gravitation

📌 Statement:

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 centers.

📌 Mathematical Formula:

F = \frac{G \cdot M \cdot m}{R^2}

F = Gravitational force
G = Universal Gravitational Constant = $6.67 \times 10^{-11} \, \text{Nm}^2/\text{kg}^2$
M = Mass of first object
m = Mass of second object
R = Distance between the centers of the two objects

🚀 Free Fall and Acceleration Due to Gravity

✅ Free Fall:

When an object falls under the influence of gravity alone (without air resistance), it is said to be in free fall.

✅ Acceleration Due to Gravity (g):

This is the acceleration produced in a freely falling object due to Earth's gravitational force.

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

On Earth, g ≈ 9.8 m/s²

Note: Acceleration due to gravity decreases with height and depth.

🔁 Motion Under Gravity Equations

When an object is falling freely:

$v = u + gt$
$s = ut + \frac{1}{2}gt^2$
$v^2 = u^2 + 2gs$

Where:

u = Initial velocity
v = Final velocity
s = Distance covered
t = Time
g = Acceleration due to gravity

For an object thrown upwards, g is taken as negative.

🧪 Difference Between Mass and Weight

Property	Mass	Weight
Definition	Amount of matter in a body	Force with which the Earth pulls an object
Unit	Kilogram (kg)	Newton (N)
Formula	—	$W = mg$
Changes with location?	No	Yes
Scalar or Vector?	Scalar	Vector

🌌 Kepler’s Laws of Planetary Motion

1. Law of Orbits
Planets move in elliptical orbits with the Sun at one focus.

2. Law of Areas
A line joining a planet and the Sun sweeps out equal areas in equal intervals of time.

3. Law of Periods
The square of the time period of revolution is directly proportional to the cube of the semi-major axis of the orbit:

T^2 \propto R^3

These laws helped Newton derive the inverse square law of gravitation.

🌠 Escape Velocity

The minimum velocity required to escape the gravitational pull of a celestial body is called escape velocity.

v_{esc} = \sqrt{\frac{2GM}{R}}

On Earth: $v_{esc} = 11.2 \, \text{km/s}$
On Moon: $v_{esc} ≈ 2.37 \, \text{km/s}$

🌀 Centripetal Force

When a body moves in a circular path, it experiences an inward force called centripetal force.

F = \frac{mv^2}{r}

Where:

m = mass of object
v = velocity
r = radius of the circular path

🧮 Example Problem – Escape Velocity on Moon

Problem:

Calculate the escape velocity on the surface of the moon.

Given:

$G = 6.67 \times 10^{-11} \, \text{Nm}^2/\text{kg}^2$
$M = 7.34 \times 10^{22} \, \text{kg}$
$R = 1.74 \times 10^6 \, \text{m}$

Solution:

v_{esc} = \sqrt{\frac{2GM}{R}} = \sqrt{\frac{2 \times 6.67 \times 10^{-11} \times 7.34 \times 10^{22}}{1.74 \times 10^6}} ≈ 2.37 \, \text{km/s}

🧠 Conceptual Questions

Q1: Will the mass and weight of an object on Mars be the same as on Earth?

Mass remains the same.
Weight is less on Mars due to lower gravity.

Q2: Why does pulling a heavy object become harder if ‘g’ doubles?

Weight increases as W = mg. So more friction and effort are needed.

Q3: A stone thrown upward takes equal time to come down. Why?

Due to uniform acceleration/deceleration by gravity, the time of ascent = time of descent.

📚 Conclusion

Gravitation is not just a force that pulls objects toward Earth—it is a cosmic force that holds the solar system together, allows us to experience weight, and governs planetary motion. Understanding gravitation not only helps in school exams but also builds a foundation for advanced physics and space science.

💡 Tip for Exams: Practice numericals, remember key formulas, and understand concept-based questions like free fall and escape velocity.

Chapter 1: Gravitation – Class 10 Science (Maharashtra Board)