Circular Motion and Gravitation

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision before your exam.

Gravitation — Key Facts Newton’s Law: F = Gm₁m₂/r²; G = 6.67×10⁻¹¹ N·m²/kg² g = GM/r² (on Earth’s surface g ≈ 9.8 m/s²); g varies with altitude and latitude Orbital velocity: v = √(GM/r) = √(gr) for orbit near surface; v ≈ 7.9 km/s Escape velocity: v_e = √(2GM/r) = √(2gr) ≈ 11.2 km/s from Earth ⚡ Exam tip: satellite in circular orbit — centripetal force = gravitational force

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🟡 Standard — Regular Study (2d–2mo)

Standard content for students with a few days to months.

Gravitation — NEET/JEE Study Guide Gravitational field: g = F/m = GM/r²; points toward mass; superposition for multiple masses Gravitational potential: V = -GM/r (negative); equipotential surfaces are spherical Kepler’s Laws: (1) orbits are ellipses with Sun at focus, (2) equal areas in equal times (L = constant), (3) T² ∝ r³ Time period: T = 2π√(r³/GM); for near-surface orbit, T ≈ 84 min; geostationary orbit T = 24h Mass of Earth: M = gR²/G where R = Earth’s radius ≈ 6400 km

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🔴 Extended — Deep Study (3mo+)

Comprehensive coverage for students on a longer study timeline.

Gravitation — Comprehensive Notes Gravitational potential energy: U = -GMm/r (from infinity to r); total mechanical energy E = KE + PE = -GMm/2r = -KE Black hole: Schwarzschild radius R_s = 2GM/c²; escape speed = c; event horizon at R_s Variation of g: with altitude g’ = g(R/(R+h))²; with depth g’ = g(1 - d/R); at equator g_min due to rotation Satellite: geostationary orbit (T=24h, h≈36,000km, equatorial), polar orbit (sun-synchronous) Inertial vs gravitational mass: experimentally equivalent to 1 part in 10¹²; foundation of equivalence principle Gravitational slingshot: Δv = 2v_planet in planet frame; used by spacecraft to gain/lose speed

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📊 JAMB Exam Essentials

Detail	Value
Questions	180 MCQs (UTME)
Subjects	4 subjects (language + 3 for course)
Time	2 hours
Marking	+1 per correct answer
Score	400 max (used for university admission)
Registration	January – February each year

🎯 High-Yield Topics for JAMB

• Use of English (Grammar + Comprehension) — 60 marks
• Biology for Science students — 40 marks
• Chemistry (Organic + Physical) — 40 marks
• Physics (Mechanics + Optics) — 35 marks
• Mathematics (Algebra + Geometry) — 40 marks

📝 Previous Year Question Patterns

• Q: “The process of photosynthesis requires…” [2024 Biology]
• Q: “The electronic configuration of Fe is…” [2024 Chemistry]
• Q: “Find the value of x if 2x + 5 = 15…” [2024 Mathematics]

💡 Pro Tips

• Use of English carries the most weight — master grammar rules and comprehension strategies
• JAMB syllabus is your Bible — questions come directly from it. Download and use it.
• Past questions are highly predictive — repeat patterns appear every year
• For Science students, Biology and Chemistry are high-scoring if you study NCERT-level content

🔗 Official Resources

• JAMB Official
• JAMB Syllabus

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