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🌍 Lesson 1 – Gravitation | Class 10 Science Part 1 | Maharashtra Board

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🔰 Introduction

Gravitation is a universal force acting between any two objects having mass.
Sir Isaac Newton discovered the law of universal gravitation, which explains that every object attracts every other object with a certain force.

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📘 Concept Notes

⚖️ Newton’s Universal Law of Gravitation

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

[
F = G \frac{m_1 m_2}{r^2}
]

Where:

• F = Force of attraction
• G = Universal Gravitational Constant = 6.67 × 10⁻¹¹ N·m²/kg²
• m₁, m₂ = Masses of two bodies
• r = Distance between their centres

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🪐 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: The line joining the planet and the Sun sweeps equal areas in equal intervals of time.
3. Law of Periods: The square of the period of revolution (T²) is directly proportional to the cube of its average distance (r³) from the Sun.
   [
   T^2 ∝ r^3
   ]

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⚙️ Acceleration due to Gravity (g)

[
g = \frac{GM}{R^2}
]

• g = 9.8 m/s² on Earth
• Decreases with height, depth and latitude
• g = 0 at Earth’s centre

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🌎 Difference between Mass and Weight

Quantity	Symbol	Unit	Constant	Remarks
Mass	m	kg	Constant	Measure of matter
Weight	W = mg	N	Changes with g	Force due to gravity

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🚀 Escape Velocity

[
v_e = \sqrt{\frac{2GM}{R}}
]
For Earth: 11.2 km/s

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🌌 Weightlessness

In space or in a freely falling lift, all objects fall with the same acceleration.
Hence, they appear weightless relative to each other.

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🧠 Important Formulas

Concept	Formula	Units
Gravitational Force	F = G m₁m₂ / r²	N
Weight	W = mg	N
Acceleration due to Gravity	g = GM / R²	m/s²
Centripetal Force	F = mv² / r	N
Escape Velocity	vₑ = √(2GM / R)	m/s
Potential Energy	U = mgh	J

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❓ Multiple Choice Questions (MCQs)

1️⃣ The force of gravitation between two objects depends on
A) their masses
B) distance between them
C) gravitational constant
D) all of these
✅ Answer: D) all of these

2️⃣ The value of G = 6.67 × 10⁻¹¹ N·m²/kg² ✅

3️⃣ The acceleration due to gravity on Earth = 9.8 m/s² ✅

4️⃣ The value of g is zero at the centre of the Earth ✅

5️⃣ The escape velocity on Earth = 11.2 km/s ✅

6️⃣ Kepler’s third law → T² ∝ r³ ✅

7️⃣ Weight of an object is maximum at the poles ✅

8️⃣ Gravitational force is always attractive ✅

9️⃣ Mass on Earth and Moon is same, but weight differs ✅

10️⃣ G was first measured by Cavendish ✅

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🧩 Exercise Questions and Answers

Q1. Match the following:

Quantity	Unit	Remark
Mass	kg	Measure of inertia
Weight	N	Depends on height
Acceleration due to gravity (g)	m/s²	Zero at the centre
Gravitational constant (G)	N·m²/kg²	Same in the entire universe

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Q2(a) Difference between mass and weight

• Mass is the quantity of matter, constant everywhere.
• Weight = gravitational force, changes with g.
• On Mars, mass same; weight less due to smaller g.

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Q2(b) Define:

i) Free fall
ii) Acceleration due to gravity
iii) Escape velocity
iv) Centripetal force

Answer:

1. Free fall → motion under gravity alone.
2. Acceleration due to gravity → rate at which a body accelerates under gravity.
3. Escape velocity → minimum speed to escape Earth’s gravity (11.2 km/s).
4. Centripetal force → force towards centre of circular path.

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Q2(c) Kepler’s Laws and Newton’s Idea

Three Kepler’s laws helped Newton realize that force ∝ 1/r², forming the inverse square law of gravitation.

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Q2(d) Stone thrown vertically upwards

Time to go up = time to come down.
t₁ = u/g and t₂ = u/g → t₁ = t₂ ✅

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Q2(e) If g doubles

Weight doubles → friction doubles → harder to pull object ✅

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Q3. Why is g = 0 at Earth’s centre?

Equal gravitational pulls act in all directions → net force = 0 ✅

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Q4. If planet is at 2R from the star, prove T₁ = 8T

T² ∝ R³ → (T₁/T)² = (2R/R)³ = 8 → T₁ = 2√2 T ✅

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Q5. Numerical Examples

(a) g = 0.4 m/s²
(b) Mass of B = 2Mₐ
(c) Weight on Moon = 8.17 N
(d) u = 100 m/s, Total time = 20 s
(e) v = 10 m/s, h = 5 m
(f) F = 2×10²⁰ N
(g) Mass of Sun = 1.96×10³⁰ kg

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🧾 Project

Take weights of five of your friends and calculate their weights on:

• Moon (g = g/6)
• Mars (g = 3.7 m/s²)

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📥 Download Study Material

🔗 Download Complete Lesson PDF (Notes + Q&A + MCQs)
👉 Click Here to Download PDF लिंक

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📚 Lesson-1-Gravitation-Notes.pdf

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Lesson-1-Gravitation-MCQs.pdf

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