The dimensional formula of the universal gravitational constant G is [M⁻¹L³T⁻²]. This is derived from Newton's law of gravitation F = Gm₁m₂/r², by expressing G in terms of fundamental quantities. The SI unit of G is N·m²/kg² = m³/(kg·s²).
Dimensional formula of G = [M⁻¹L³T⁻²].
Derived from G = Fr²/(m₁m₂) using dimensions of F, r, and m.
SI unit of G = N·m²·kg⁻² = m³·kg⁻¹·s⁻².
Value of G = 6.674 × 10⁻¹¹ N·m²/kg².
G is universal and constant; g varies with location.
g = GM/R²; dimensional formula of g = [LT⁻²].
Newton's Law of Gravitation: F = Gm₁m₂/r²
Solving for G: G = F·r² / (m₁·m₂)
Substituting dimensions: • [F] = [MLT⁻²] (force) • [r²] = [L²] (distance squared) • [m₁·m₂] = [M²] (product of masses)
[G] = [F][r²] / [m₁m₂] = [MLT⁻²][L²] / [M²] = [ML³T⁻²] / [M²] = [M⁻¹L³T⁻²]
Dimensional formula of G = [M⁻¹L³T⁻²]
SI unit of G: N·m²/kg² = (kg·m·s⁻²)·m²/kg² = m³·kg⁻¹·s⁻² = m³/(kg·s²)
Value of G: G = 6.674 × 10⁻¹¹ N·m²·kg⁻² = 6.674 × 10⁻¹¹ m³·kg⁻¹·s⁻²
G was first measured by Henry Cavendish in 1798 using a torsion balance experiment.
SI unit: N·m²·kg⁻² or m³·kg⁻¹·s⁻² CGS unit: dyne·cm²·g⁻² = 6.674 × 10⁻⁸ dyne·cm²·g⁻²
Key points about G: • G is a universal constant — same everywhere in the universe. • Very small value (10⁻¹¹) — gravity is the weakest of the four fundamental forces. • G ≠ g. (g = 9.8 m/s² is gravitational acceleration on Earth's surface; G is the universal constant.) • G has dimensions; g has dimensions [LT⁻²].
G (Universal Gravitational Constant): • Value: 6.674 × 10⁻¹¹ N·m²/kg² • Dimensional formula: [M⁻¹L³T⁻²] • Universal — same everywhere • Does not depend on location
g (Acceleration due to gravity): • Value on Earth's surface: 9.8 m/s² • Dimensional formula: [LT⁻²] = [M⁰L¹T⁻²] • Varies with location (height, depth, latitude) • g = GM/R² (where M = mass of Earth, R = radius of Earth)
Relation: g = GM_earth / R_earth² = (6.674×10⁻¹¹ × 6×10²⁴) / (6.4×10⁶)² = (4.0044×10¹⁴) / (4.096×10¹³) ≈ 9.77 m/s² ≈ 9.8 m/s²
Dimensional formula of g: [g] = [GM/R²] = [M⁻¹L³T⁻²][M]/[L²] = [LT⁻²] ✓
[M⁻¹L³T⁻²]. Derived from G = Fr²/(m₁m₂): [G] = [MLT⁻²][L²]/[M²] = [M⁻¹L³T⁻²].
N·m²·kg⁻² (or equivalently m³·kg⁻¹·s⁻²).
G = 6.674 × 10⁻¹¹ N·m²/kg². First measured by Henry Cavendish in 1798.
G (6.674×10⁻¹¹ N·m²/kg²) is the universal gravitational constant — same everywhere. g (9.8 m/s²) is acceleration due to gravity on Earth's surface — varies with location. g = GM/R².
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