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Playbook

Gravitation

17 q · 12% HARD. F=Gm₁m₂/r², g=GM/R², escape velocity √(2gR), orbital period T²∝R³ (Kepler 3rd), weightlessness in free-fall. The 'planet-scaled' ratio question is the recurring HARD shape.

questions in the bank
17
tagged HARD
12%
subtopic(s)
3
worked examples
2

When you’ll see it

An F = Gm₁m₂/r² calculation, a planet-scaled g/v_esc/T comparison, a Kepler's-3rd orbital-period ratio, or a weightlessness explanation.

How this chapter is tested

17 q in 10 years · 12% HARD. Three subtopics: Gravitational Field and Potential (7 q), Newton's Law of Gravitation (6 q), Orbits Kepler Escape (4 q). The chapter is formula-light (4 formulas) but ratio-trap heavy.

Surface gravity g = GM/R². Escape velocity v_esc = √(2gR) = √(2GM/R). Kepler's third law T² ∝ R³. The recurring HARD shape: 'a planet has R = R_earth/2 and density 4× Earth's, find escape speed' — needs you to expand M = ρ·(4/3)πR³ THEN plug into v_esc formula. The factors cancel: v_esc = same as Earth.

Weightlessness in orbit: the astronaut and the station are both in FREE FALL toward Earth, accelerating at the same rate, so the astronaut feels no normal force from the station floor. This is not 'no gravity' — gravity is still there, providing the centripetal force for the orbit.

The sub-skills

The rules and habits that decide whether you get a question right.

  • Newton's law of gravitation plug-in

    F = Gm₁m₂/r² between two point masses. G = 6.67×10⁻¹¹. r is centre-to-centre distance.

  • Surface g for any planet

    g = GM/R². With M = (4/3)πR³ρ, g = (4/3)πGRρ. So g ∝ R·ρ.

  • Escape velocity scaling

    v_esc = √(2gR) = √(2GM/R) = √((8/3)πGR²ρ). So v_esc ∝ R·√ρ. Doubling R doubles v_esc (with ρ fixed). Quadrupling ρ doubles v_esc.

  • Kepler's third law ratio

    T² ∝ R³. Ratio form: T₁/T₂ = (R₁/R₂)^(3/2). If R doubles, T multiplies by 2^(3/2) = 2.83.

2 worked examples from the bank

Real past-year questions illustrating the playbook. Click to reveal options + solution.

Example 1GravitationHARD
Escape speed from the Earth is close to 11.2 km s−1s^{-1}. On another planet whose radius is half of the Earth's radius and whose mass density is four times that of the Earth, the escape speed in km s−1s^{-1} will be close to :

[Q84 · Apr · 2024]

Example 2GravitationMODERATE
One year at a planet is 8 times as large as compared to one year at Earth. Which one is correct about the planet's orbit?

[Q66 · Apr · 2026]

Traps to expect

Distractor shapes specific to this chapter. The page-wide Traps section covers the bank-level patterns.

  • Planet-scaling: keeping ρ and R separate

    If R scales by k and ρ by m, then M scales by m·k³, NOT m·k. Forgetting the R³ factor inside mass is the recurring trap. Always expand M = (4/3)πR³ρ symbolically.

  • Weightlessness = no gravity

    Wrong. Weightlessness = no NORMAL FORCE because everything is falling at the same rate. Gravity is still acting; it's providing the centripetal force for the orbit.

Drill every gravitation question

17 questions from the bank, scoped to 3 bundled subtopics.

Drill the 17 questions

Related playbooks

Often paired with this one — drill these next if you found the worked examples above tractable.