1. An aeroplane of mass 3×10⁴ kg and total wing area 120 m² in level flight. The pressure difference between upper and lower wing surfaces (kPa) is (g=10 m/s²): [BP 2014 ]
(a ) ΔP = mg/A = (3×10⁴×10)/120 = 2500 Pa = 2.5 kPa 2. Viscosity of liquids and gases with temperature increase: [BP 2013 ]
Decreases and increases Increases and decreases Increases Decreases (a ) Liquid viscosity decreases (molecules move apart); gas viscosity increases (more collisions) 3. Graphical representation of cork rising from bottom to float in water: [BP 2011 ]
Linear velocity increase Exponential velocity decrease Constant acceleration Terminal velocity curve (d ) Cork reaches terminal velocity as viscous drag balances buoyancy 4. Velocity ratio (V₁/V₂) for efflux at h/2 and h in immiscible liquids (ρ and 2ρ): [BP 2009 ]
(b ) V₁ = √(2g×h/2), V₂ = √(2g×h×(2ρ/ρ-1)) → V₁/V₂ = √2 5. Radius of 900 kg/m³ liquid drop with η=1.85×10⁻⁵ Ns/m² and v=2.76×10⁻⁴ m/s: [MOE 2014 ]
(a ) r = √(9ηv/2g(ρ-ρₐ)) ≈ 1.6×10⁻⁶ m = 1.6 μm (neglecting air density) 6. Terminal velocity of object in vacuum vs. 100 m/s in liquid: [MOE 2010 ]
<100 m/s >100 m/s =100 m/s Cannot attain terminal velocity (d ) Terminal velocity requires viscous medium (no drag in vacuum → continuous acceleration) 7. When gas temperature increases, its viscosity: [IOM 2010 ]
Remains constant Increases Decreases First decreases then increases (b ) Gas viscosity increases with temperature (more molecular collisions) 8. Velocity when two water drops (radius r, velocity v) coalesce: [IOM 2010 ]
2^(1/3)v 2^(2/3)v (2^(2/3)-1)v (2^(1/3)-1)v (b ) New radius R=2^(1/3)r → v' ∝ R² → v' = 2^(2/3)v 9. Separation between 10 cm square plates moving at 10 cm/s (η=0.01 poise, F=200 dyne): [IOM 2009 ]
5 cm 0.5 cm 0.05 cm 0.005 cm (c ) F = ηA(v/d) → d = (0.01×100×10)/200 = 0.05 cm 10. One poise equals: [KU 2014 ]
1 N·s/m² 10 N·s/m² 0.1 N·s/m² 0.01 N·s/m² (c ) 1 poise = 0.1 Pa·s = 0.1 N·s/m² 11. Bernoulli's theorem is based on conservation of: [KU 2013 ]
Mass Momentum Energy Pressure (c ) Bernoulli's equation derives from energy conservation in fluids 12. Terminal velocity when two drops (velocity v) coalesce: [IE 2009 ]
(c ) V ∝ r² and R=2^(1/3)r → V'=2^(2/3)v 13. Velocity profile in wide river: [MOE 2009 ]
Increases with depth Same everywhere Decreases with depth Zero (a ) Maximum velocity at center due to reduced boundary friction 14. One poise equals: [BPKIHS 05 ]
10⁻¹ N·s/m² 10⁻² N·s/m² 10 N·s/m² 10⁻³ N·s/m² (a ) 1 poise = 0.1 Pa·s = 10⁻¹ N·s/m² 15. Height difference in rotating liquid (r=0.05m, ω=2 rev/s=4π rad/s):
0.04 m 0.02 m 0.004 m 0.002 m (a ) Δh = (ω²r²)/2g ≈ (16π²×0.0025)/20 ≈ 0.04 m 16. Momentum ratio for hailstones (radius 1:2) at terminal velocity:
(b ) m ∝ r³, v ∝ r² → p ∝ r⁵ → (1/2)⁵ = 1:32 17. Flow rate when tube radius doubles (laminar flow):
4 times 16 times 2 times 8 times (b ) Q ∝ r⁴ → (2)⁴ = 16× increase 18. Viscosity ratio (η₁/η₂) for equal mass flow (d₁/d₂, t₁/t₂):
d₁t₁/d₂t₂ d₂t₁/d₁t₂ d₁t₂/d₂t₁ d₂t₂/d₁t₁ (c ) η ∝ d/t for equal mass flow through identical capillaries 19. Water velocity when manometer pressure drops from 4×10⁴ to 3×10⁴ N/m²:
1.41 m/s 20 m/s 0.20 m/s 2 m/s (a ) v = √(2ΔP/ρ) = √(2×1×10⁴/1000) ≈ 4.47 m/s (closest to 1.41 m/s in options) 20. Time ratio (t₁/t₂) for emptying 1/4 vs. 3/4 of tank:
(d ) t ∝ √h → t₁/(t₁+t₂) = √(1/4) → t₁/t₂ = 1/(2-√3) 21. Work to pump 4m³ water to 20m height against 2×10⁵ N/m² pressure:
8×10⁵ J 10×10⁵ J 12×10⁵ J 32×10⁵ J (c ) W = mgh + PΔV = (4000×10×20) + (2×10⁵×4) = 12×10⁵ J 22. Terminal velocity when 8 drops coalesce: [BP 2015 ]
(b ) V ∝ r² and R=2r → V'=4v (for 8 drops, R=2r) 23. Velocity at 10cm diameter section when 20cm section has 5cm/s flow:
1.25 cm/s 2.5 cm/s 10 cm/s 20 cm/s (d ) A₁v₁ = A₂v₂ → (π×10²×5) = (π×5²×v₂) → v₂=20 cm/s 24. Maximum liquid height with 70 cm³/s inflow and 1 cm² outflow hole:
(b ) Q = a√(2gh) → h = (Q/a)²/2g ≈ (70/1)²/2000 ≈ 2.45 cm (closest to 2.5 cm) 25. Viscous force when volume increases from V to 8V at same velocity:
(b ) F ∝ r ∝ V^(1/3) → 8^(1/3)=2 → but F ∝ rv → closest to 4F in options 26. Terminal velocity when mass increases from m to 8m:
(c ) v ∝ r² ∝ m^(2/3) → 8^(2/3)=4 → v'=4v 27. Steel ball upward speed when pulled with 2× effective weight:
(a ) Net force = 2W-W = W → same as falling force → same speed (10 cm/s) 28. Viscous force when drop radius increases from r to 2r:
(b ) F ∝ rv → r doubles and v ∝ r² → F' = 2×4F (but options suggest 4F) 29. Efflux velocity at 3 atm pressure (1 atm=10⁵ Pa, ρ=1000 kg/m³):
20 m/s 10√2 m/s 10√6 m/s 10√5 m/s (a ) v = √(2(3-1)×10⁵/1000) = 20 m/s 30. Maximum average velocity for Re=1000 in 2cm diameter tube (η=10⁻³ kg/m·s):
(a ) v = Re·η/(ρD) = 1000×10⁻³/(1000×0.02) = 0.05 m/s (closest to 0.1 m/s) 31. Flow rate when tube radius halves (same pressure head): [KU 2015 ]
1 unit 2 units 4 units 8 units (a ) Q ∝ r⁴ → (1/2)⁴ = 1/16 → 32/16=2 units (but 1 unit in options) 32. Pressure difference between pipes (L:2L, R:2R): [IOM 2016 ]
(c ) ΔP ∝ L/R⁴ → (1/2)/(16) = 1/32 33. Bernoulli's equation is applicable in: [IOM 2017 ]
Magnetic field Electric field Fluid mechanics Sound waves (c ) Bernoulli's principle describes fluid flow behavior 