Chapter 7 - The Earth and Gravitation
Part 1: Core Definitions & Formulas (Guaranteed Marks)
Term
Definition
Key Formula
Gravitation
The force of attraction between any two objects in the universe. (e.g.,
Sun and Earth, you and your book).
F = G * (m₁m₂) / d²
Gravity
The specific gravitational force where one of the objects is the Earth.
It's the force that pulls objects towards the Earth's center.
(Same as above, where
m₁ is Earth's mass)
Mass (m)
The amount of matter in an object. It is a constant value and never
changes, no matter where you are.
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Weight (W)
The force with which the Earth pulls an object towards its center. It is
not constant and changes with location.
W=m*g
Acceleration due to The acceleration produced in a freely falling body due to Earth's gravity.
Gravity (g)
It's the rate at which velocity increases per second for a falling object.
g = GM / d² (where M is
Earth's mass)
Key Variables:
•
F = Force of attraction (Unit: Newton, N)
•
G = Universal Gravitational Constant (Memorize this value: 6.673 x 10⁻¹¹ Nm²kg⁻²)
•
m₁, m₂ = Mass of the two objects (Unit: kilogram, kg)
•
d = Distance between the centers of the objects (Unit: meter, m)
•
W = Weight (Unit: Newton, N)
•
g = Acceleration due to gravity (Unit: m/s²)
Part 2: The Most Important Concepts (For MCQs & Short Questions)
1. Mass vs. Weight - The Classic Comparison
Feature
Mass
Weight
Definition
Amount of matter
Force of gravity on the matter
Nature
Scalar quantity (only magnitude) Vector quantity (magnitude & direction)
Change
Never changes with location
Changes with location (because 'g' changes)
Unit
Kilogram (kg)
Newton (N)
At Center of Earth Remains the same
Becomes Zero
2. Why 'g' (and therefore Weight) Changes - MASTER THIS!
The value of g = GM / d². Since G and M (Earth's mass) are constant, 'g' only depends on 'd' (distance from Earth's
center).
•
•
Reason 1: Earth's Shape
o
The Earth is not a perfect sphere. It's slightly flattened at the poles and bulges at the equator.
o
At the Poles: Distance 'd' is minimum. So, 'g' is maximum (≈ 9.83 m/s²). Weight is maximum.
o
At the Equator: Distance 'd' is maximum. So, 'g' is minimum (≈ 9.78 m/s²). Weight is minimum.
Reason 2: Altitude & Depth
o
Going Up (Mountain): Distance 'd' increases. So, 'g' decreases. Weight decreases.
o
Going Down (Mine): 'g' also decreases. At the very center of the Earth, g = 0, so Weight = 0.
Summary Table of 'g' Values to Memorize:
Location
Value of 'g'
Weight
Poles
Maximum (≈ 9.83 m/s²) Maximum
Equator
Minimum (≈ 9.78 m/s²) Minimum
Standard Value (for calculations) 9.8 m/s²
m x 9.8
Center of Earth
Zero (0)
Zero (0)
3. Weightlessness
•
Definition: The state where an object has no apparent weight. It happens when there is no reaction force acting
on the object.
•
In a Freely Falling Lift: Both you and the lift fall at the same rate (a=g). You don't press on the floor, so you feel
weightless. Apparent weight is zero.
•
In an Orbiting Spacecraft: The astronaut and the spacecraft are in a constant state of free fall around the Earth.
This causes the feeling of weightlessness. It is NOT because gravity is zero in space! Gravity is what keeps
them in orbit.
Part 3: Top Questions & Calculations (Practice These!)
1. The "Distance Change" Question (100% will come in MCQ):
The gravitational force F is inversely proportional to the square of the distance (F ∝ 1/d²).
•
If distance 'd' is doubled (x2), Force 'F' becomes 1/4th (1/2²).
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If distance 'd' is tripled (x3), Force 'F' becomes 1/9th (1/3²).
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If distance 'd' is halved (x½), Force 'F' becomes 4 times stronger (1/(½)²).
2. Calculating Weight on Earth:
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Question: A body has a mass of 20 kg. What is its weight?
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Answer: W = mg = 20 kg × 9.8 m/s² = 196 N.
3. Calculating Mass or Weight on the Moon:
•
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Question: A body weighs 600 N on Earth.
o
(a) What is its mass?
o
(b) What is its weight on the Moon?
o
(c) What is its mass on the Moon?
Answer:
o
(a) m = W/g = 600 N / 9.8 m/s² ≈ 61.22 kg.
o
(b) Weight on Moon = Weight on Earth / 6 = 600 N / 6 = 100 N.
o
(c) Mass does not change. Mass on the Moon is still 61.22 kg.
4. Why does a stone fall to the ground but the Earth doesn't move towards the stone?
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Answer: According to Newton's law, both the stone and the Earth attract each other with the exact same force.
However, acceleration a = F/m. Since the Earth's mass (m) is enormous, its acceleration is practically zero, so it
doesn't move. The stone's mass is tiny, so it accelerates significantly and falls.
Final Advice: Read these notes 3-4 times. Focus on the bolded words. Mentally solve the practice calculations. You are
now fully equipped to ace your test. Good luck