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Newton's Law of Gravitation, Field and Potential

Free notes · JEE Main Physics

Formulas

F=Gm1m2r2,g=GMr2,V=−GMrF = \frac{G m_1 m_2}{r^2}, \qquad g = \frac{GM}{r^2}, \qquad V = -\frac{GM}{r}

Gravitational force, field intensity and potential of a point mass M

U=−GMmrU = -\frac{GMm}{r}

Gravitational potential energy of mass m at distance r from M

Key points

Worked example

Find the gravitational field intensity at a height h = R above the Earth's surface (R = 6.4 × 10⁶ m, M = 6.0 × 10²⁴ kg, G = 6.67 × 10⁻¹¹).

  1. r = R + h = 2R = 1.28 × 10⁷ m
  2. g = GM/r² = (6.67e-11 × 6.0e24) / (1.28e7)² = 4.0e14 / 1.638e14 ≈ 2.44 m/s²
  3. Check: g' = g/4 = 9.8/4 ≈ 2.45 m/s² ✓ (height R halves gravity to a quarter)

Answer: g ≈ 2.45 m/s²