PhysicsPHY 04
Gravitation & Fluid Mechanics
Kepler's laws, escape velocity, Bernoulli's theorem, surface tension, viscosity
NCERT XI Ch.8+10
NCERT Ref
Concept Core
Essential theory — everything NCERT tests on Gravitation & Fluid Mechanics
GRAVITATION — KEPLER'S LAWS
1st Law: Planets orbit in ellipses with Sun at one focus.
2nd Law: Equal areas in equal time (angular momentum conservation). Fastest at perihelion.
3rd Law: T² ∝ R³. (T²/R³ = constant for all planets around same star).
GRAVITATIONAL QUANTITIES
Escape velocity: ve = √(2GM/R) = √(2gR) ≈ 11.2 km/s (Earth).
Orbital velocity: vo = √(GM/R) = √(gR) ≈ 7.9 km/s. Note: ve = √2 × vo.
Variation of g: decreases with height (g' = g(R/(R+h))²) and depth (g' = g(1−d/R)). g = 0 at centre.
BERNOULLI'S THEOREM
P + ½ρv² + ρgh = constant (along a streamline). Energy conservation for ideal fluid flow.
Applications: Venturimeter (flow measurement), Magnus effect (spinning ball), aerofoil lift, Bunsen burner, carburetor, spinning top. High velocity = low pressure.
SURFACE TENSION & VISCOSITY
Surface tension T = F/L (N/m). Excess pressure inside drop: 4T/r (soap bubble, two surfaces), 2T/r (liquid drop, one surface).
Capillary rise: h = 2T cosθ/(rρg). Viscosity: η = Fr/(Av). Stokes' law: F = 6πηrv. Terminal velocity: vt = 2r²(ρ−σ)g/(9η).
SATELLITES & POTENTIAL ENERGY
Gravitational PE: U = −GMm/r. Total energy of satellite: E = −GMm/(2r). KE = GMm/(2r). PE = −GMm/r.
Geostationary satellite: T = 24 hrs, height ≈ 36,000 km, orbit in equatorial plane. Polar satellite: low orbit, sun-synchronous.
Fact & Formula Vault
High-yield facts, numbers, and formulas
Key Formulae
v_e = √(2GM/R) = 11.2 km/s
v_o = √(GM/R) = 7.9 km/s
v_e = √2 × v_o
T² ∝ R³ (Kepler's 3rd)
Surface Tension
Drop excess pressure = 2T/r
Bubble excess pressure = 4T/r
Capillary rise: h = 2Tcosθ/rρg
T decreases with temperature
Viscosity
Stokes law: F = 6πηrv
Terminal vel: vt = 2r²(ρ−σ)g/9η
η decreases with temp (liquids)
η increases with temp (gases)
Worked Examples
NEET-style questions solved step-by-step
EASYEscape velocity from Earth's surface is approximately:▾
Escape velocity from Earth's surface is approximately:
11.2 km/s. v_e = √(2GM/R) = √(2gR) = √(2 × 9.8 × 6.4×10⁶) ≈ 11.2 km/s. Independent of mass of object.
MEDIUMThe excess pressure inside a soap bubble of radius r is:▾
The excess pressure inside a soap bubble of radius r is:
Soap bubble has TWO surfaces (inner + outer). Each surface contributes 2T/r pressure. Total excess pressure = 4T/r. A liquid drop (one surface) = 2T/r.
HARDA planet orbits at distance 4R from Sun compared to another at R. Ratio of periods?▾
A planet orbits at distance 4R from Sun compared to another at R. Ratio of periods?
T² ∝ R³ (Kepler's 3rd). T₁²/T₂² = R₁³/R₂³ = (4R)³/R³ = 64. T₁/T₂ = 8. Outer planet's period = 8 × inner.
Mistake DNA
Common NEET traps for this chapter
⚠ Soap bubble vs liquid drop
Drop has ONE free surface → 2T/r. Soap bubble has TWO (inner + outer) → 4T/r.
✓ Fix: Drop = 2T/r. Bubble = 4T/r. (Bubble = 2× drop)
⚠ v_e vs v_o
v_e = √2 × v_o. Escape velocity is √2 times orbital velocity at same radius.
✓ Fix: v_e/v_o = √2. Both independent of projectile mass.
⚠ Viscosity vs temperature
For LIQUIDS: viscosity decreases with temperature. For GASES: viscosity increases with temperature.
✓ Fix: Liquids: η↓ with T. Gases: η↑ with T.
Chapter Intelligence
Exam data and last-minute strategy
NEET Frequency
2–3 Q/year. Kepler's 3rd law (T²∝R³), escape velocity, soap bubble vs drop pressure, terminal velocity, geostationary satellite are most common.
High-Yield
v_e = 11.2 km/s. v_e = √2 × v_o. Bubble = 4T/r. Drop = 2T/r. T²∝R³. Terminal velocity increases with r².
Strategy
Memorise key formulae. Kepler's 3rd law problems just need ratio method — no absolute values needed. Bubble/drop distinction is a guaranteed 1-marker.
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