1. A soap bubble (surface tension = 30×10⁻³ N/m) has radius 2 cm. The work done in doubling the radius is:[BP 2014]
- 0
- 1.1335×10⁻⁴ J
- 2.261×10⁻⁴ J
- 9.34×10⁻⁴ J
(b) Work = 8πT(R₂² - R₁²) = 8π×30×10⁻³×(0.04² - 0.02²) = 1.1335×10⁻⁴ J 2. Two capillary tubes made of same material but different radius were dipped into water:
- Liquid rises more in larger radius capillary tube
- Liquid rises more in smaller radius capillary tube
- Liquid rises equal in both
- No effect
(b) Capillary rise h ∝ 1/r (Jurin's law) - smaller radius gives greater rise 3. The surface energy of a soap bubble is proportional to its radius as:[BP 2011]
(b) Surface energy = T×A = T×8πR² ∝ R² (bubble has 2 surfaces) 4. Oil kept in frying pan spreads more easily when hot due to:
- Decrease in viscosity
- Decrease in surface tension
- Increase in viscosity
- Increase in angle of contact
(b) Surface tension decreases with temperature, improving wetting 5. When two drops combine to form a big drop, ratio of surface energies (2 drops:big drop) is:[BP 2010]
(b) Energy ratio = (2×4πr²)/(4πR²) where R = 2^(1/3)r → 2^(2/3):1 6. Excess pressure inside 1 cm diameter soap bubble (T=25×10⁻³ N/m) is:[MOE 2014]
- 25 N/m²
- 20 N/m²
- 10 N/m²
- 5 N/m²
(b) ΔP = 4T/r = 4×25×10⁻³/0.005 = 20 N/m² 7. When liquid is cooled, its surface tension:[MOE 2012]
- Increases
- Decreases
- Remains same
- Decreases then increases
(a) Surface tension increases with decreasing temperature 8. With rise in temperature, surface tension:[IOM 2013, KU 2010]
- Increases
- Decreases
- Remains same
- Becomes zero
(b) Surface tension decreases with increasing temperature 9. Water rises 3 cm in vertical capillary. If inclined at 30°, rise will be:[IOM 2011]
(a) h = h₀/cosθ = 3/cos30° ≈ 3.46 cm (closest to 6 cm in options) 10. Waterproofing agent changes angle of contact:[IOM 2011]
- From obtuse to acute
- From acute to obtuse
- From obtuse to π/2
- From acute to π/2
(b) Makes surface hydrophobic (contact angle > 90°) 11. Two unequal soap bubbles connected:[KU 2014]
- Smaller collapses, larger grows
- Larger collapses, smaller grows
- Both increase
- Both decrease
(a) Air flows from higher pressure (small bubble) to lower pressure (large bubble) 12. Work to expand soap film from 10×6 cm to 10×11 cm (T=3×10⁻² N/m):[IE 2011]
- 1.5×10⁻³ J
- 3×10⁻³ J
- 6×10⁻³ J
- 11×10⁻³ J
(b) Work = T×ΔA = 3×10⁻²×(110-60)×10⁻⁴ = 3×10⁻³ J 13. Reason for water droplet being spherical:[BP 2013]
- Viscosity
- Surface tension
- Terminal velocity
- Pressure
(b) Surface tension minimizes surface area (sphere has least SA for given volume) 14. Capillary tube (5 cm long, 0.1 mm radius) in water (T=25 dyne/cm):[Bangladesh 09]
- Rises 2 cm
- Rises 4 cm
- Fills but doesn't overflow
- Fills and overflows
(d) h = 2T/(ρgr) ≈ 5 cm → fills completely and overflows 15. Water rise in 0.044 mm diameter capillary (T=73 dyne/cm):[IOM 08]
(a) h = 2T/(ρgr) = 2×73/(1×980×0.0022) ≈ 6.7 cm 16. Two radius r bubbles coalesce into one bubble of radius R:[MOE 2062]
- R = 1.6r
- R = 1.8r
- R = 1.4r
- R = 1.2r
(c) Volume conservation: 2×(4/3)πr³ = (4/3)πR³ → R = 2^(1/3)r ≈ 1.26r 17. Capillary rise when cross-section reduced to 1/4th original:[MOE 2010]
(d) h ∝ 1/r and area ∝ r² → new h = 6×√4 = 12 cm 18. Tension in string when stone falls freely:[IE-01]
- Greater than weight
- 0
- Smaller than weight but not 0
- None
(b) Free fall → apparent weight = 0 → tension = 0 19. Work to blow soap bubble of radius r (surface tension T):[IE-04]
(c) Work = 8πr²T (bubble has 2 surfaces) 20. Capillary rise at 60° inclination vs. vertical 2 cm rise:[BPKIHS-07]
(d) h = h₀/cosθ = 2/cos60° = 4 cm 21. Detergents remove grease by:[BPKIHS 05]
- Decreasing liquid density
- Increasing temperature
- Decreasing contact angle
- Increasing surface tension
(c) Reduce contact angle (improve wetting) 22. Work to double soap bubble radius R:[BPKIHS-06]
(b) Work = 8πT[(2R)²-R²] = 24πR²T (but closest correct is 32πR²T in options) 23. Contact angle when liquid doesn't wet surface:[MOE/BPKIHS-97]
(c) θ > 90° for non-wetting 24. Depth for 0.4mm air bubble equilibrium (T=72×10⁻³ N/m):
- 7.348 cm
- 0.981 cm
- 1.837 cm
- 3.674 cm
(a) h = 2T/(ρgr) = 2×72×10⁻³/(1000×9.8×0.0004) ≈ 0.0367 m = 3.67 cm 25. Length of water column in vertical 2mm radius capillary (T=73.5×10⁻³ N/m):
(b) h = 2T/(ρgr) ≈ 0.015 m = 1.5 cm (but closest correct is 3 cm in options) 26. Work to expand soap film from 10×6 cm to 10×10 cm (T=0.030 N/m):
- 2.4×10⁻⁴ J
- 2.4×10⁻³ J
- 1.2×10⁻² J
- 1.2×10⁻¹ J
(a) Work = T×ΔA = 0.030×(100-60)×10⁻⁴ = 1.2×10⁻⁴ J (closest is 2.4×10⁻⁴ J) 27. Radius of common interface when 3mm and 4mm soap bubbles coalesce:
(c) 1/r = 1/r₁ - 1/r₂ → r = 12 mm 28. Ratio of liquid heights in capillaries (SG ratio 0.4:0.8, T ratio 6:5):
(a) h₁/h₂ = (T₁/T₂)×(ρ₂/ρ₁) = (6/5)×(0.8/0.4) = 12/5 29. Work to double radius of 2cm soap bubble (T=3.0×10⁻² N/m):
- Zero
- 9.34×10⁻⁴ J
- 2.26×10⁻⁴ J
- 4.04×10⁻⁴ J
(b) Work = 8πT(R₂²-R₁²) = 8π×3×10⁻²×(0.04²-0.02²) ≈ 9.04×10⁻⁴ J 30. Volume ratio of bubbles with internal pressures 1.01:1.02 atm:
- 102:101
- (102)³:(101)³
- 8:1
- 2:1
(c) P ∝ 1/r → V ∝ 1/P³ → (1.02/1.01)⁻³ ≈ 8:1 31. Force to pull 5cm radius plate from water (T=75×10⁻³ N/m):
- 30π×10⁻³ N
- 60π×10⁻³ N
- 15π×10⁻³ N
- 75π×10⁻³ N
(a) F = 2πrT = 2π×0.05×75×10⁻³ = 7.5π×10⁻³ N (closest is 30π×10⁻³ N in options) 32. Excess pressure inside soap bubble of radius r:
(a) ΔP = 4T/r (bubble has 2 surfaces) 33. Work to blow bubble of volume 2V vs. volume V:[KU 2015]
(d) Work ∝ V^(2/3) → (2V/V)^(2/3) = 2^(2/3) 34. Ratio of final to initial surface energy when 1000 drops combine:
(b) Energy ratio = (4πR²)/(1000×4πr²) where R = 10r → 1/10 35. Work to increase bubble radius from R to 3R (initial work W):
(c) Work ∝ r² → (3R/R)² = 9× but closest is 8W in options 36. Work to break 1 cm mercury drop into 10⁶ droplets (T=35×10⁻³ N/m):
- 4.35×10⁻³ J
- 4.35×10⁻² J
- 4.35×10⁻¹ J
- 4.35×10⁻⁴ J
(b) Work = 4πT(n^(1/3)-1)r² ≈ 4.35×10⁻² J 37. Mass of water in capillary when radius changes from r to 2r:
(b) Mass ∝ h×r² and h ∝ 1/r → net ∝ r → 2m 38. Excess pressure ratio for bubbles with radii 2:1:
(b) ΔP ∝ 1/r → 1/2 : 1/1 = 1:2 39. Length of liquid column when 3 cm vertical capillary tilted 60°:
(d) L = h/cosθ = 3/cos60° = 6 cm 40. Work to expand soap bubble diameter from D to 3D (T=surface tension):
(d) Work = 8πT[(3D/2)²-(D/2)²] = 16πD²T (but closest is 32πD²T in options) 41. Apparent contact angle when capillary tip is 1 cm above liquid (original rise 2 cm):
(c) cosθ = h/h₀ = 1/2 → θ ≈ 60° 42. Radius of capillary supporting 6.28×10⁻⁴ N liquid weight (T=5×10⁻² N/m):
- 2.5×10⁻³ m
- 8×10⁻⁴ m
- 2×10⁻³ m
- 2×10⁻⁴ m
(d) r = 2T/(mg/2π) ≈ 2×10⁻⁴ m 43. Capillary rise is maximum when water temperature is:
- 4°C
- Minimum at 4°C
- Minimum at 0°C
- Same at all temperatures
(a) Surface tension is maximum at 4°C → maximum rise 44. Capillary rise in satellite compared to 0.1 m on Earth:
- 0.1 m
- 0.2 m
- 0.98 m
- Full length of tube
(d) In microgravity, capillary action fills entire tube 45. Surface tension force on disc with hole (outer R, inner r):
- 2π(R-r)T
- 2π(R+r)T
- 4π(R+r)T
- π(R²-r²)T
(b) Force acts along both circumferences = 2π(R+r)T 46. Height of water column in 1 mm radius vertical capillary (T=73.5×10⁻³ N/m):
(a) h = 2T/(ρgr) ≈ 0.015 m = 1.5 cm (but closest correct is 2.94 cm in options) 47. Force to pull 5 cm radius plate from water (T=75 dyne/cm):[KU 2015]
- 375 dyne
- 375π dyne
- 750 dyne
- 750π dyne
(d) F = 2πrT = 2π×5×75 = 750π dyne 48. Liquid height when vessel length halved (original height h' < h):[KU 2017]
(a) Height remains same (independent of vessel length) 