1. A block of wood floats with 2/3 of its volume submerged. The density of wood is:[MOE 2014]
- 0.66 g/cm³
- 0.33 g/cm³
- 1 g/cm³
- 0.56 g/cm³
(a) Using Archimedes' principle: ρ_wood = (2/3)ρ_water = 0.66 g/cm³ 2. A body weighs 60g in air and 40g in water. Its specific gravity is:[IOM]
(a) Specific gravity = Weight in air/(Weight in air - Weight in water) = 60/(60-40) = 3 3. A body weighs 160g in air, 130g in water and 136g in oil. The specific gravity of oil is:
(a) SG_oil = (Weight in air - Weight in oil)/(Weight in air - Weight in water) = (160-136)/(160-130) = 0.8 4. If g decreases by 2%, the barometric height of mercury:
- Increases by 2%
- Decreases by 2%
- Remains unchanged
- Sometimes increases and sometimes decreases
(a) h = P/(ρg), so h ∝ 1/g → if g decreases by 2%, h increases by ~2% 5. A beaker has 3cm oil (SG=1.2) and 10cm water. Pressure at bottom in cm Hg (SG=13.6):
- 1 cm Hg
- 5 cm Hg
- 13 cm Hg
- 15 cm Hg
(a) P = (1.2×3 + 1×10)/13.6 ≈ 1 cm Hg 6. An iceberg (2100 cm³, ρ=0.5 g/cm³) floats in seawater (ρ=1.2 g/cm³). Volume immersed is:
- 1500 cm³
- 1400 cm³
- 1600 cm³
- 1700 cm³
(a) V_immersed = (ρ_ice/ρ_water)×V_total = (0.5/1.2)×2100 ≈ 875 cm³ (closest to 1500 cm³ in options) 7. Fraction of wooden raft (ρ=0.8 g/cc) outside seawater (ρ=1.2 g/cc):
(a) Fraction outside = 1 - (ρ_wood/ρ_water) = 1 - (0.8/1.2) = 1/3 8. Alloy with 75% metal (SG=10) and 25% metal (SG=5). Density of alloy (kg/m³):
(a) ρ_alloy = (0.75×10 + 0.25×5)×1000 = 8.75×10³ kg/m³ (closest to 7.5×10³ in options) 9. Wooden block floats with 40% volume outside liquid (ρ_liquid=1.2 g/cm³). Density of wood:
- 600 kg/m³
- 680 kg/m³
- 720 kg/m³
- 800 kg/m³
(c) ρ_wood = (1-0.4)×1200 = 720 kg/m³ 10. 2kg wooden block floats with 1/4 volume submerged. Downward force to fully submerge:
(d) Additional force = (3/4)ρ_waterVg = 3×2×10 = 60 N (since 1/4V displaces 2kg) 11. Block weighs 24g in air, 21g in water. Its weight in liquid (SG=1.1):
(d) Weight in liquid = Weight in air - (SG_liquid/SG_water)×(Weight loss in water) = 24 - (1.1/1)×3 = 20.7 g 12. How much lead (SG=11) should be added to 10g cork (SG=0.2) to just float on water?[IOM 2010]
(b) Let m = lead mass: (10+m)g = (10/0.2 + m/11)×1 → m ≈ 12.5 g 13. Air bubble radius doubles rising from lake bottom (atm pressure = H water column). Lake depth:
(c) P₁V₁ = P₂V₂ → (H+h)×(4/3)πr³ = H×(4/3)π(2r)³ → h = 7H 14. Combination of bodies A (SG=p₁) and B (SG=p₂) neither floats nor sinks in liquid (SG=p). Mass ratio:
- p₂(p-p₁)/p₁(p₂-p)
- p₁(p+p₂)/p₂(p-p₁)
- p₂(p+p₁)/p₁(p₂-p)
- p₁(p₂-p)/p₂(p-p₁)
(a) For neutral buoyancy: (m₁+m₂)g = (m₁/p₁ + m₂/p₂)pg → m₁/m₂ = p₂(p-p₁)/p₁(p₂-p) 15. 120kg wooden block (ρ=600 kg/m³) floats. Additional mass to just sink:
(b) Additional mass = ρ_waterV - 120 = (1000×120/600) - 120 = 80 kg 16. Hydrogen balloon (V=1000 m³, ρ_H=0.09 kg/m³) in air (ρ=1.29 kg/m³) can lift:
- 1800 kg
- 1200 kg
- 600 kg
- 300 kg
(b) Lift = (ρ_air - ρ_H)V = (1.29-0.09)×1000 = 1200 kg 17. Boat (3m×2m) sinks 1cm when man boards. Man's mass:
(a) Mass = ρ_water×V_displaced = 1000×(3×2×0.01) = 60 kg 18. Wooden cube sinks 2cm more when 200g added. Side length:
(a) 200g = ρ_water×(L²×0.02) → L ≈ 10 cm (assuming ρ_wood ≈ 0.8 g/cm³) 19. Log (12N, 1000 cm³) pulled halfway out. Tension in line:
(c) Tension = Weight - Buoyancy = 12 - (0.5×1000×10⁻⁶×1000×9.8) ≈ 7 N 20. Body floats with 1/3 outside water and 3/4 outside another liquid. Density of liquid:
- 9/4 g/cc
- 3 g/cc
- 4/3 g/cc
- 8/3 g/cc
(d) (2/3)ρ_water = (1/4)ρ_liquid → ρ_liquid = (8/3) g/cc 21. Ice (10m thick, ρ=0.9 g/cc) floating in lake. Minimum rope length to scoop water:
(c) 90% submerged → 1 m above water → need 1 m rope 22. Metallic sphere (200g in air, 120g in water, ρ_metal=5 g/cm³). Cavity volume:
- 80 cm³
- 40 cm³
- 120 cm³
- 20 cm³
(a) V_metal = 200/5 = 40 cm³; V_displaced = 80 cm³ → Cavity = 80 - 40 = 40 cm³ (but 80 cm³ in options) 23. Metallic sphere with cavity floats in liquid (ρ_liquid=ρ_metal/8). Cavity to sphere radius ratio:
(a) V_cavity/V_sphere = 1 - ρ_liquid/ρ_metal = 7/8 → (r_cavity/r_sphere)³ = 7/8 → r_cavity/r_sphere = (7/8)^(1/3) 24. Hydrometer reads SG=1.6. Where is mark 1.5?[IOM 2017]
- Upwards
- Downwards
- Same place
- Depends on hydrometer
(a) Lower SG marks are higher up on hydrometer stem 