Notes For All Chapters – Science & Technology Part I Class 10
Gravitation
1. Introduction to Gravitation
Definition: Gravitation is a universal force that acts between all objects in the universe, attracting them towards each other.
Discovery: Sir Isaac Newton discovered gravitation by observing an apple falling vertically downward, leading him to conclude that the Earth attracts objects towards its center.
2. Key Concepts
Gravitational Force
Acts between any two objects, e.g., Earth and an apple, or Earth and the Moon.
Directed towards the center of the Earth for objects on or near its surface.
Extends to greater distances, affecting objects like the Moon, planets, and the Sun.
Force and Motion
A force is required to change the speed or direction of an object’s motion.
Newton’s Laws of Motion:
First Law: An object remains at rest or in uniform motion unless acted upon by a force.
Second Law: Force = mass × acceleration (F = ma).
Third Law: For every action, there is an equal and opposite reaction.
3. Circular Motion and Centripetal Force
Centripetal Force: A force that acts on an object moving in a circular path, directed towards the center of the circle.
Example: A stone tied to a string moving in a circle experiences centripetal force towards the center. If the string is released, the stone moves tangentially due to its velocity.
Application: The Moon orbits the Earth due to the Earth’s gravitational force acting as the centripetal force. Similarly, planets orbit the Sun.
4. Kepler’s Laws of Planetary Motion
First Law: Planets move in elliptical orbits with the Sun at one focus.
Second Law: The line joining a planet and the Sun sweeps equal areas in equal intervals of time.
Third Law: The square of a planet’s period of revolution (T²) is proportional to the cube of its mean distance from the Sun (r³), i.e., T² ∝ r³ or T²/r³ = constant.
5. Newton’s Universal Law of Gravitation
Every object in the universe attracts every other object with a force proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
Formula: F = G (m₁m₂ / d²)
F = gravitational force
m₁, m₂ = masses of the two objects
d = distance between their centers
G = Universal Gravitational Constant (6.673 × 10⁻¹¹ N m² kg⁻²)
Implications:
Doubling the mass of one object doubles the force.
Doubling the distance reduces the force to one-fourth.
For non-spherical objects, the force acts between their centers of mass.
6. Acceleration Due to Gravity (g)
Definition: The acceleration produced in an object due to the Earth’s gravitational force, directed towards the Earth’s center.
Formula: g = GM / R²
G = Universal Gravitational Constant
M = Mass of the Earth (6 × 10²⁴ kg)
R = Radius of the Earth (6.4 × 10⁶ m)
Value of g on Earth’s surface ≈ 9.77 m/s² (approximately 9.8 m/s²).
Variation of g:
On Earth’s Surface: Varies slightly due to Earth’s non-spherical shape. Highest at poles (9.832 m/s²), lowest at equator (9.78 m/s²).
With Height: g decreases as height increases (r increases in g = GM/r²).
With Depth: g decreases as the effective mass of Earth contributing to gravity reduces.
At Earth’s Center: g = 0, as gravitational forces cancel out.
On Other Planets: g varies with the planet’s mass and radius (e.g., on the Moon, g ≈ 1/6th of Earth’s g).
7. Mass and Weight
Mass: Amount of matter in an object, measured in kg, a scalar quantity, constant everywhere.
Weight: Force with which the Earth attracts an object, W = mg, measured in Newtons, a vector quantity, varies with g.
Example: A 75 kg person weighs 735 N on Earth (g = 9.8 m/s²) but only 122.5 N on the Moon (g ≈ 1.63 m/s²).
8. Free Fall
Definition: Motion of an object under the influence of gravity alone, with initial velocity u = 0 and acceleration a = g.
Equations of Motion for Free Fall:
v = gt
s = (1/2)gt²
v² = 2gs
For objects thrown upwards, acceleration is –g (opposite to velocity).
Example: Galileo’s experiment showed that objects of different masses fall at the same rate in a vacuum, as g is independent of mass.
9. Gravitational Potential Energy
Definition: Energy stored in an object due to its position in a gravitational field.
Formula: PE = –GMm / (R + h) (negative because PE is zero at infinite distance).
For small heights (h << R), PE ≈ mgh, assuming g is constant.
10. Escape Velocity
Definition: The minimum velocity required for an object to escape Earth’s gravitational pull and reach infinite distance.
Formula: v_esc = √(2GM/R) = √(2gR)
On Earth: v_esc ≈ 11.2 km/s
On Moon: v_esc ≈ 2.37 km/s (due to lower mass and radius).
Conservation of Energy: Total energy (kinetic + potential) at the surface equals zero at infinite distance.
11. Weightlessness in Space
Objects and astronauts in orbiting spacecraft appear weightless because they are in free fall, moving with the same velocity as the spacecraft under Earth’s gravity.
12. Gravitational Waves
Predicted by Einstein in 1916, these are waves in the fabric of space-time caused by massive accelerating objects.
Detected in 2016 by LIGO, providing new insights into the universe.
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