Topic: Fluid Mechanics
A crane is used to lower weights into the sea (sea water density = 1025 kg/m³) for an underwater construction project. What is the percentage reduction in the tension in the rope of the crane due to a rectangular 0.4m × 0.4m × 3m concrete block (density = 2300 kg/m³) when it is completely immersed in water compared to the tension in the rope when it was suspended in air
- A. 45%
- B. 55%
- C. 65%
- D. 75%
Answer: A. 45%
Explanation: Tension in air T1 = weight of block = rho_block * V * g. Tension in water T2 = weight - buoyancy = (rho_block - rho_water) * V * g. The ratio of tension in water to air is T2/T1 = (2300 - 1025) / 2300 = 1275 / 2300 ≈ 0.554 (or 55.4%). The percentage reduction is (1 - 0.554) * 100 = 44.6%, which is approximately 45%.