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Gravitation — Question 3

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Question 3

What is the magnitude of the gravitational force between the earth and a 1 kg object on its surface? (Mass of the earth is 6 × 1024 kg and radius of the earth is 6.4 × 106 m.)

Answer

Mass of the body (m) = 1 kg

Mass of the earth (M) = 6 × 1024 kg

Radius of the Earth (R) = 6.4 × 106 m

G = 6.67 x 10-11 Nm2kg-2

According to the formula for gravitational force we know,

F = G MmR2\dfrac{\text{M}\text{m}}{\text{R}^2}

Substituting we get,

F=6.67×10−11×6×1024×1(6.4×106)2=6.67×10136.4×6.4×1012=9.77 N≈9.8 N\text{F} = \dfrac{6.67 \times 10^{-11}\times 6 \times 10^{24} \times 1}{(6.4 \times 10^6)^2} \\[1em] = \dfrac{6.67 \times 10^{13}}{6.4 \times 6.4 \times10^{12}} \\[1em] = 9.77 \text{ N} \approx 9.8 \text{ N}

Hence, magnitude of the gravitational force = 9.8 N

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Science | Chapter 9: GravitationWeb Content — Quick Reference

Chapter 9: Gravitation — Quick Reference

universal law gravity mass weight pressure buoyancy Archimedes principle relative density

Quick Revision Points

  • F = Gm₁m₂/r² (G = 6.674 × 10⁻¹¹ N·m²/kg²)
  • g = GM/R² = 9.8 m/s² (Earth); g on Moon ≈ g/6
  • Mass (kg, constant) vs Weight (N = mg, varies with location)
  • Pressure P = F/A (Pa = N/m²); Fluid pressure P = hρg
  • Archimedes: buoyant force = weight of displaced fluid
  • Float if density < fluid density; Sink if density > fluid density
  • Relative density = density of substance / density of water (no unit)
Exam Tips for Chapter 9
  • Read the detailed chapter notes for complete coverage of all NCERT topics.
  • Practice all NCERT in-text and back exercise questions — they are frequently asked in exams.
  • Focus on comparison tables, diagrams, and definitions — these are high-scoring areas.
  • For numericals (if applicable), practice at least 20 problems of varying difficulty.
  • Refer to the practice question bank (200+ questions) for thorough preparation.
Related Resources
  • Detailed Notes: ch09-gravitation.html
  • Practice Questions: 100+ questions with answers in 05-practice-questions/
  • Chapter Test: 30-mark test paper in 06-tests/chapter-tests-30marks/
  • Formula Sheet: Complete formula reference in 03-teacher-aid/formula-sheet.html
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