Topic: Fluid Mechanics
A cylindrical body of diameter 2 m and height 1.5 m having a mass of 2 tonnes and floats in sea water with its axis vertical. A lighting equipment is placed on the body such that the water level is at least 0.5 m below the top surface. What is the maximum mass of the electrical equipment that can be placed on the body. (The specific gravity of sea water may be taken as 1.02 and pi = 3.14)
- A. 252 kg
- B. 750 kg
- C. 1202 kg
- D. 275 kg
Answer: C. 1202 kg
Explanation: Maximum depth of immersion = 1.5 - 0.5 = 1.0 m. Maximum displaced volume V = (pi/4) * D² * depth = (3.14/4) * (2^2) * 1.0 = 3.14 m³. Maximum buoyant force = V * rho_water * g = 3.14 * 1020 * g = 3202.8 * g Newtons. This means the cylinder can support a total mass of 3202.8 kg. Subtracting the cylinder's own mass (2000 kg), the maximum mass of the equipment is 3202.8 - 2000 = 1202.8 kg.