Gravitation and Planetary Motion

Overview

This lecture covers all the main concepts related to gravitation, Newton's law of gravitation, buoyancy, Archimedes' principle, pressure, mass versus weight, with theory and numericals.

Gravitation and Gravitational Force

• Gravitation is the attractive force between any two objects.
• Newton's law: The force between any two objects is proportional to the product of their masses and inversely proportional to the square of the distance between them.
• Formula: F = G M1 M2 / R^2, where G is the universal gravitational constant.
• Unit of G: Newton meter²/kilogram² (N m²/kg²)

Centripetal Force and Planetary Motion

• Planets and satellites revolve in circular orbits due to centripetal force.
• Centripetal force pulls the object towards the center of the circle.

Acceleration Due to Gravity (g)

• When an object falls freely, it experiences an acceleration g = 9.8 m/s².
• The value of g is higher on land, lower at higher altitudes and underground.
• g is lower at the equator and higher at the poles.

Mass Versus Weight

• Mass = amount of matter in the body (in kilograms), Weight = force due to gravity (in Newtons).
• Weight = Mass × g, mass is constant everywhere, weight depends on g.
• Mass is a scalar quantity, weight is a vector.

Free Fall and Motion Equations

• In free fall, a is replaced by g; for objects thrown downward, g is negative.
• Key formulas: v = u + gt, h = ut + ½gt², v² = u² + 2gh

Pressure, Thrust, and Their Applications

• Pressure = Thrust/Area, unit Pascal.
• More pressure on smaller area, less on larger area.
• Sharp knife, wide tractor tires, camel's broad feet are based on these principles.

Fluid Pressure, Buoyancy, Archimedes' Principle

• Pressure increases with both fluid depth and density.
• Buoyant force = upward force equal to the weight of displaced fluid.
• Archimedes' principle: Buoyant force = weight of displaced fluid.
• Sinking-floating depends on density—higher density = sinking, equal = floating.

Kepler's Laws of Planetary Motion

• Planets revolve around the sun in elliptical orbits.
• They sweep equal areas in equal times.
• Time² ∝ Radius³ (The period of a planet is proportional to the cube of the radius of its orbit)

Key Terms & Definitions

• Gravity (गुरुत्वाकर्षण) — Attractive force acting between all mass particles.
• Universal Gravitational Constant (G) — Constant used in the formula for F.
• Acceleration due to gravity (g) — Acceleration applied by Earth on an object.
• Mass (द्रव्यमान) — Amount of matter in an object.
• Weight (भार/वजन) — Gravitational force on an object, W = mg.
• Buoyant Force (बायंट फोर्स) — Upward force on an object immersed in a fluid.
• Pressure (दाब) — Force applied per unit area on a surface, P = F/A.

Action Items / Next Steps

• Prepare revision notes on Archimedes' principle, mass-weight difference, Kepler's laws, free fall.
• Practice example-based numericals.
• Remember the values and units of G and g.
• Comment for the next lecture topic.