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Gravitation formula sheet

Every formula in the Gravitation chapter for JEE Main, with one line on when it applies. Topic 1 is open to everyone; sign in free to read all 35 and download the PDF.

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How we count: 7× asked means 7 past JEE Main questions in the PrepWiser bank needed that formula, and "last" is the latest year one appeared. ★ marks formulas asked 8 or more times.

Newton's law and superposition

Newton's law of gravitation
4× asked, last 2025
F=Gm1m2r2,G=6.67×10−11 N m2kg−2F=\frac{Gm_1m_2}{r^2},\qquad G=6.67\times10^{-11}\ \text{N m}^2\text{kg}^{-2}
Point or spherical masses, rr between centres. Fixed total mass: FF largest for equal masses.
Rod on its axis
F=GMmd(d+L)F=\frac{GMm}{d(d+L)}
Rod MM, length LL; mm at distance dd from the near end. Not GMm/(d+L/2)2GMm/(d+L/2)^2.
Superposition
5× asked, last 2026
F⃗net=∑iGm miri2 r^i\vec F_{\text{net}}=\sum_i\frac{Gm\,m_i}{r_i^2}\,\hat r_i
Add as vectors; cancel symmetric sideways parts. Square corner: (2+1/2)Gm2/a2(\sqrt2+1/2)Gm^2/a^2.
Two masses circling each other
5× asked, last 2023
Gm2(2r)2=mv2r ⇒ v=Gm4r\frac{Gm^2}{(2r)^2}=\frac{mv^2}r\ \Rightarrow\ v=\sqrt{\frac{Gm}{4r}}
Separation 2r2r. Three on a triangle of side aa: v=Gm/av=\sqrt{Gm/a}. Four on a square: v2=(22+1)GM/4Rv^2=(2\sqrt2+1)GM/4R.
Binary stars
2× asked, last 2021
ω2=G(m1+m2)d3,r1=m2 dm1+m2\omega^2=\frac{G(m_1+m_2)}{d^3},\qquad r_1=\frac{m_2\,d}{m_1+m_2}
Both circle the CM with the same ω\omega; T=2π/ωT=2\pi/\omega.
Ring on its axis
2× asked, last 2021
E=GMx(R2+x2)3/2,V=−GMR2+x2E=\frac{GMx}{(R^2+x^2)^{3/2}},\qquad V=-\frac{GM}{\sqrt{R^2+x^2}}
Zero at the centre; largest at x=R/2x=R/\sqrt2.
Arc at its centre
1× asked, last 2024
F=2GmλRsin⁡ϕ2,λ=MRϕF=\frac{2Gm\lambda}{R}\sin\frac\phi2,\qquad \lambda=\frac{M}{R\phi}
Arc angle ϕ\phi (rad). Semicircle: 2Gmλ/R2Gm\lambda/R; full ring: 0.
Sphere with a cavity
2× asked, last 2025
F=Ffull−Fremoved,Mremoved=M(rR)3F=F_{\text{full}}-F_{\text{removed}},\qquad M_{\text{removed}}=M\left(\frac rR\right)^3
MM = uncut mass. If MM is the mass left: Mr3/(R3−r3)Mr^3/(R^3-r^3). Inside the cavity: uniform 4πGρd/34\pi G\rho d/3.

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Practise Gravitation

27 more formulas in 5 topics

Acceleration due to gravity and its variation, Gravitational field and potential, Gravitational PE and escape speed, Satellites and orbital motion and Kepler's laws. Read the first part free. Sign in free with Google to read the rest and download the PDF.

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Acceleration due to gravity and its variation

  • gg at the surface10×
  • Variation with height15×
  • Variation with depth15×
  • Equal height and depth (exact)
  • Latitude and rotation6×
  • Tunnel through the earth1×

Gravitational field and potential

  • Point mass4×
  • Thin spherical shell2×
  • Uniform solid sphere (inside)5×
  • Non-uniform density2×

Gravitational PE and escape speed

  • PE of a system4×
  • Change in PE with height6×
  • Escape speed18×
  • Escape from a height or orbit3×
  • Launched below escape speed4×
  • Neutral point between two bodies3×

Satellites and orbital motion

  • Orbital speed8×
  • Orbit shape from launch speed
  • Time period10×
  • Angular momentum of a satellite4×
  • Energy of a satellite4×
  • Energy to change orbit3×
  • Geostationary satellite3×
  • Weightlessness in orbit

Kepler's laws

  • Law of areas4×
  • Perihelion and aphelion5×
  • Kepler's third law16×

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About 160 past JEE Main questions from this chapter, with instant answer checking and step-by-step solutions where available. Free, and you can start without signing up.

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