Gravitation and Elasticity
What this domain tests
Gravitation and Elasticity tests Newton's law of gravitation, variation of g, orbital and escape speeds, Kepler's laws, stress and strain, Young's modulus and elastic energy.
Core rules
- F = Gm1m2/r²; g = GM/R² at the surface.
- At height h: g_h = g/(1 + h/R)²; at depth d: g_d = g(1 − d/R).
- Orbital speed v = √(GM/r); escape speed v_e = √(2GM/R) = √(2gR) ≈ 11.2 km s⁻¹.
- Kepler's third law: T² ∝ r³.
- Stress = F/A; strain = ΔL/L; Young's modulus Y = stress/strain.
- Elastic PE per unit volume = ½ × stress × strain.
Worked example
A wire of length 2.0 m and area 1.0×10⁻⁶ m² stretches by 1.0 mm under a 100 N load. Stress = 100/1.0×10⁻⁶ = 1.0×10⁸ Pa. Strain = 1.0×10⁻³/2.0 = 5.0×10⁻⁴. Young's modulus Y = 1.0×10⁸/5.0×10⁻⁴ = 2.0×10¹¹ Pa, typical of steel.
Traps
- Using the same formula for g at height and at depth.
- Thinking escape speed depends on the mass of the projectile; it does not.
- Confusing stress with force and strain with extension.
- Forgetting that Young's modulus is a property of the material, not of the particular wire.