Physics notesMechanicsGravitation
Independent topic page
Work with U and V (potential) rather than force magnitude alone; energy and Kepler’s law then decide orbital and escape stems in one ledger.
01. g⃗ = −GM r̂ /r² outside a spherical mass (or at surface with R). Inside a uniform sphere, g∝r. Potential V=−GM/r (V∞=0); U=mV.
02. Escape from surface: ½mv_e² − GMm/R = 0 ⇒ v_e=√(2GM/R)=√(2gR) if g=GM/R².
03. Circular orbit: centripetal = gravity ⇒ v=√(GM/r); T²=(4π²/GM)r³ (Kepler III for Sun-centred or Earth satellites with M≫m).
04. Geostationary: equatorial, same sense as Earth rotation, T=24 h sidereal day matching, fixed r from Kepler III. Binding energy for circular orbit is GMm/(2r).
05. Field and potential are different objects: g = −∇V (or −dV/dr radially). Superposition holds for both; energy of a mass m in a field is mV with your zero of V stated (usually ∞).
06. Orbital mechanics: centripetal demand v²/r = GM/r² for circular orbits; total E=−GMm/(2r). Escape needs E≥0 from the surface or from the orbit you start in—state the starting PE carefully.
07. Shell theorems: outside a uniform sphere acts as point mass; inside a shell field is zero. Density and cavity problems are superposition, not new constants.
Official · 2026
Official syllabus points for Gravitation only — not the full Mechanics portion map. Portion hub: Mechanics · Mechanics analysis.
No topic-specific exclusions flagged — finish the unit points below for Gravitation.
Source: https://jeeadv.ac.in/documents/jee-advanced-2026-syllabus.pdf
Exam focusGravitational field/potential, Kepler, satellites, and escape velocity.
Syllabus points
Do / check
2020–2026 paper weight
Topic match inside parent portion Mechanics (32.3% of Physics tags). Stats below are portion backdrop; matched subtopics show where Gravitation sits.
Portion-wide type/difficulty mix lives on the Mechanics analysis — not repeated here so this page stays on Gravitation.
01. Dominant subtopics: Rotation (21), Mixed (16), Projectile/Kinematics (10), Gravitation (7).
Cross-topic stems
Advanced rarely asks a chapter in isolation. These are tagged multi-idea Physics stems that touch Gravitation — practise the knowledge bridge, not only the single-chapter drill.
Step 1: relate arc lengths so the small disks roll without slipping on the large circumference (geometry of contact). Step 2: convert path radius R+r into orbital and spin rates (ω/51-type ratios). Step 3: close the remaining angular gap 2π − Δθ to get the meeting time τ.
Easy to use the wrong Δθ (2/51 vs 4/51) if relative rolling sense is mishandled.
Always draw contact velocities and write v = ωr for every rolling interface before algebra.
Why methods matter
Region-wise field/potential and circular-orbit energy relations organise almost every gravity stem.
Potential is easier than vector g for assemblies and energy questions.
Do thisAdd scalar V from each spherical/point piece; then g=−∇V or use symmetry for g.
Potential is easier than vector g for assemblies and energy questions.
Two masses: V at a point is −GM₁/r₁−GM₂/r₂; equipotential ≠ equal field.
One criterion covers surface escape, escape from orbit, and ‘minimum energy to remove’.
Do thisEscape and binding questions: require E≥0 at infinity relative to V∞=0.
One criterion covers surface escape, escape from orbit, and ‘minimum energy to remove’.
From circular orbit, need ΔE = +GMm/(2r) to reach E=0.
Avoids inserting G and M when only ratios are asked.
Do thisFor two orbits about same centre, (T₁/T₂)²=(a₁/a₂)³.
Avoids inserting G and M when only ratios are asked.
If a doubles, T grows by 2√2.
Prevents using GM/r² inside cavities or thick shells wrongly.
Do thisOutside: as point mass at centre; inside a thin shell: g=0, V=constant=−GM/R.
Prevents using GM/r² inside cavities or thick shells wrongly.
Uniform sphere cavity problems: superposition of full sphere minus imaginary sphere.
Processed examples
Read the impact line first. Then notice which family/model was chosen. The solution is written the way your rough sheet should look in the hall.
Find orbital speed for a circular orbit of radius 2R about Earth. Take g at surface and R known: express in √(gR).
This stem rewards early recognition of the orbital mechanics / kepler model.
Model chosenGM=gR²; v=√(GM/r).
Answer√(gR/2)
Takeaway: Replace GM using surface g.
Potential at the surface of a uniform sphere is −V₀. Find potential at the centre.
This stem rewards early recognition of the field and potential of spherical mass model.
Model chosenInside uniform sphere V(r)=−(GM/(2R))(3−r²/R²).
Answer−(3/2)V₀
Takeaway: Potential is continuous and deepest at the centre.
A satellite in circular orbit of radius 2R (planet radius R) is to be transferred to a circular orbit of radius 8R via a Hohmann ellipse. Find the total Δv required in terms of g and R (g=GM/R²).
This Advanced-level variation couples hidden constraints with the satellite transfer and energy change model.
Model chosenHohmann: two burns at periapsis and apoapsis using vis-viva.
AnswerΔv=√(gR)[√0.8−√(1/2)+√(1/8)−√0.05]
Takeaway: Transfer costs are differences between circular and elliptical speeds at the same r.
Reusable models
Advanced stems cluster. Name the family in 10–15s, write the fast model, then run the same path. Do not invent a new plan each time.
Looks likePoint outside/inside uniform sphere or shell
Fast modelOutside: like point mass; inside shell E=0; inside solid E∝r.
Recognition fixes the model before arithmetic begins.
Do not start blind expansion or casework before identifying the governing model.
Looks likeCircular orbit, period, energy, or escape
Fast modelUse GMm/r² = mv²/r and E=−GMm/(2r) for circular.
Recognition fixes the model before arithmetic begins.
Do not start blind expansion or casework before identifying the governing model.
Looks likeRaise orbit, geostationary, or binding energy
Fast modelΔE from E=−GMm/(2a) between orbits.
Recognition fixes the model before arithmetic begins.
Do not start blind expansion or casework before identifying the governing model.
Looks likeUniform sphere self-energy or dismantling work
Fast modelU_self = −(3/5)GM²/R for uniform sphere (standard result).
Recognition fixes the model before arithmetic begins.
Do not start blind expansion or casework before identifying the governing model.
Hall timing
Underline given data, unknowns and constraints. Name the mechanical model before recalling any formula; discard relations whose assumptions are already broken.
Draw axes, free-body or energy/impulse diagram. Write governing equations symbolically with consistent sign and reference.
Solve algebraically as far as possible; substitute numbers only once. Keep vectors, components and units on the rough sheet.
Check dimensions, limiting cases and physical sense. For multi-correct, test every option independently rather than forcing one narrative.
After the model is locked
g = GM/r² toward centre
r≥R spherical mass
V = −GM/r (V_∞=0); U = −GMm/r
Point mass / outside sphere
v_e = √(2GM/r) from distance r
Reach infinity with E≥0
v_c = √(GM/r); T = 2π√(r³/GM)
Satellite, M≫m
E = −GMm/(2r) circular; E=−GMm/(2a) ellipse
Total mechanical energy
T² ∝ a³ / M_central (fixed central mass)
Period–orbit size ratios
g′ ≈ g(1−2h/R) for h≪R above surface; inside uniform: g(r)=GMr/R³
Near-Earth or interior
T=2π√(r³/GM_E)=1 sidereal day
Geo orbit radius
Make it automatic