Gravitation • Force & Fields
Newton’s law · g variation · Weight vs Mass · Free fall · 50 MCQs + 50 Numericals (click to reveal)
Core Concepts: Gravitation & Gravity
Newton’s Universal Law
Every particle attracts every other with force: F = G·m₁·m₂ / r²
G = 6.67×10⁻¹¹ N·m²/kg² (universal constant)
📌 Gravitational force is always attractive, acts along the line joining centers.
🪐 Acceleration due to gravity (g)
g = G·M / R² (Earth’s surface) ≈ 9.8 m/s². Varies with altitude, depth, latitude.
Weight vs Mass
Mass – scalar, constant (kg). Weight = m·g (vector, N). Weight changes with g, mass is invariant.
Free fall: Motion under only gravity. Equations: v=u+gt, h=ut+½gt², v²=u²+2gh.
Applications:卫星 orbits, lift problems, well depth, coin&feather experiment.
Applications:卫星 orbits, lift problems, well depth, coin&feather experiment.
📈 Variation of g: with altitude: g’ = g(1 – 2h/R); with depth: g’ = g(1 – d/R); at poles > equator due to rotation. Free fall acceleration independent of mass (Galileo).
50 MCQs on Gravitation, g, Weight & Free Fall
Click “show answer” after trying each
50 Numericals (Gravitation, g, Weight, Free Fall)
Step-by-step hidden solutions
Quick Reference: Formulas & Applications
Key Formulae
- F = G m₁m₂/r²
- g = GM/R² → gsurface
- Weight W = mg
- galtitude = g(1 – 2h/R)
- gdepth = g(1 – d/R)
- Orbital velocity vₒ = √(GM/r)
Free fall applications
- Time to hit ground: t = √(2h/g)
- Velocity from height: v = √(2gh)
- Object in lift (apparent weight)
- Well depth measurement (echo time)
- Gravitational slingshot
Weight on Moon = (1/6) Weight on Earth because gmoon = 1.62 m/s²