Motion Under Gravity Notes with PDF

These notes are your ultimate revision weapon to reviseMotion Under Gravity. We’ve distilled years of previous exam questions (PYQs) into one powerful, concise resource. Everything you need to know, nothing you don’t.

• PYQs, Decoded: All key concepts from past exams, organized and simplified.
• Revise in Record Time: Short, precise, and designed for last-minute review.
• Focus on What Matters: Master high-probability topics and boost your confidence.
• Free PDF to download.

Historical Understanding of Gravity

• Early Proponents
  • Brahmagupta: A 7th-century Indian mathematician and astronomer from Bhinmal, Rajasthan.
  • In his work, ‘Brahmasphuta Siddhanta,’ he declared that all objects are attracted to the Earth.
  • He anticipated the concept of gravity before Isaac Newton.
• Formal Theory
  • Isaac Newton: Formally propounded the Universal Law of Gravitation in 1687.
  • Published his theory in the book “Mathematical Principles of Natural Philosophy.”
  • The Law: Every object in the universe attracts every other object with a force.
  • This force is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
  • Formula: F = G (m₁m₂ / r²), where G is the Gravitational Constant.

The Universal Law of Gravitation and Its Principles

• Core Principle
  • The gravitational force between two objects increases if their masses increase.
  • The gravitational force between two objects decreases if the distance between them increases.
  • Example: If the distance between two objects (e.g., Earth and Sun) is doubled, the gravitational force becomes one-fourth of its original value.

Effects of Gravity on Weight and Sensation

• Sub-topic: Weight vs. Mass
  • Mass is the amount of matter in a body and remains constant everywhere.
  • Weight is the force of gravity acting on a mass. It changes with location.
  • Example: On the Moon, gravity is 1/6th of Earth’s gravity, so a person’s weight there is 1/6th of their weight on Earth.
• Variation on Earth
  • Gravity is not the same at every point on Earth’s surface due to its oblate spheroid shape (flattened at poles, bulging at equator).
  • The value of gravitational acceleration (g) is maximum at the poles and minimum at the equator.
  • Therefore, a body is heaviest at the poles and lightest at the equator.
• Weightlessness
  • Weightlessness is the sensation of having no weight, often described as zero gravity.
  • It occurs when an object is in free fall and there is no supporting force.
  • Astronauts in orbit experience weightlessness (microgravity) because they are in a continuous state of free fall around the Earth.
  • Apparent Weight in a Lift:
    • A person feels heavier when a lift accelerates upwards.
    • A person feels lighter when a lift accelerates downwards.

Motion Under Gravity (Free Fall)

• Acceleration Due to Gravity (g)
  • On Earth, the constant acceleration for a freely falling body is 9.8 m/s².
  • The velocity of a freely falling body after time t is calculated by v = u + gt (where u is initial velocity, often 0).
    • Example: After 3 seconds, velocity = 0 + (9.8 × 3) = 29.4 m/s.
  • In a vacuum (ignoring air resistance), all objects, regardless of their mass or material (e.g., wood, wax, iron), fall at the same rate.
• The Role of Air Resistance
  • In the presence of air, objects with larger surface areas experience more air resistance.
  • Therefore, in air, a heavier, more compact object (like an iron ball) will fall faster than a lighter, less dense object (like a wooden ball).

Gravity in Celestial Contexts

• Satellites and Orbits
  • Artificial satellites do not fall to Earth because gravity provides the necessary centripetal force for their orbital motion.
  • For a geosynchronous satellite, the centripetal force is provided by the Earth’s gravitational pull.
  • An object (like an apple) released inside an orbiting spaceship will continue to move along with the spaceship at the same speed due to inertia.
• Escape Velocity
  • Escape velocity is the minimum speed needed for an object to break free from a planet’s gravitational pull without further propulsion.
  • Earth’s escape velocity is 11.2 km/sec.
  • An object thrown with a speed less than this (e.g., 8 km/sec) will return to Earth.
• Moon’s Lack of Atmosphere
  • The Moon has no atmosphere because its gravitational pull is weak.
  • The escape velocity for gas molecules on the Moon is less than their average speed, so they escape into space.
• Earth’s Orbital Motion
  • The Earth travels in its orbit at approximately 4,400 km per hour.
  • We do not feel this motion because our relative speed with respect to the Earth is zero (we are moving with the Earth).

Gravity and Earth’s Phenomena

• Sub-topic: Earthquakes
  • A destructive earthquake involves ground accelerations that can exceed the acceleration due to gravity (> 980 cm/sec² or > 9.8 m/sec²).
• Stability of Objects
  • An object remains stable as long as the vertical line through its center of gravity falls within its base.
  • Example: The Leaning Tower of Pisa does not fall because its center of gravity is still within its base.

Pendulums and Gravity

• Time Period
  • The time period of a pendulum depends on its length (T = 2π√(l/g)).
  • It does not depend on the mass of the bob.
• Effect of Temperature
  • In summer, a pendulum expands (length increases), which increases its time period, causing the clock to lose time (run slow).
  • In winter, a pendulum contracts (length decreases), which decreases its time period, causing the clock to run faster.
• Motion and Energy
  • At the mean position, a pendulum bob has maximum velocity, zero acceleration, and maximum kinetic energy.
  • At the extreme position, the bob has zero velocity, maximum acceleration, and maximum potential energy.
  • In each oscillation cycle, the bob attains any given velocity (less than the maximum) twice.
  • The amplitude of oscillation decreases with time due to air resistance.
• Practical Example (Swing)
  • When a person stands up on a swing, the effective length of the pendulum decreases.
  • This shortens the time period, making the swing oscillate faster.

Gravity and Fundamental Forces

• The Four Fundamental Forces of Nature:
  1. Gravity
  2. Electromagnetism
  3. Weak Nuclear Force
  4. Strong Nuclear Force
• Gravity is the weakest of the four fundamental forces.
• The Strong Nuclear Force is the strongest and holds protons and neutrons together inside an atom’s nucleus.
• The Weak Nuclear Force is responsible for radioactivity.
• Electromagnetism acts only on particles with an electric charge.

Miscellaneous Effects of Gravity

• Flame in Microgravity
  • In a state of weightlessness (microgravity), a candle flame becomes spherical.
  • The existence of a teardrop-shaped flame on Earth is due to gravity causing convection currents (hot air rises). Without gravity, this effect vanishes.
• Gravity and Mass
  • If Earth’s gravity disappeared, an object’s weight would become zero, but its mass would remain the same.

Motion Under Gravity Know More About:

• Motion Under Gravity – Old Year Questions
• Motion Under Gravity One Liner Questions & Answers