Final answer:
To determine the draught of the cylindrical drum in sea water, we apply the principle of flotation and calculate the total weight of the drum and diesel oil it contains. We then find the volume of sea water displaced by equating it to this total weight and translate that back into a depth. The correct draught is 55 cm.
Step-by-step explanation:
To find the draught (submerged depth) of the cylindrical drum in sea water, we need to use the principle of flotation, which states that the weight of the fluid displaced by a floating object is equal to the weight of the object. First, we need to find the total weight of the drum and the diesel oil it contains.
The drum's volume can be calculated using the diameter (which is 68 cm, thus radius is 34 cm or 0.34 m) and height (80 cm or 0.8 m) in this formula: Volume = πr²h. However, this total volume is not necessary since we're provided with the volume of diesel oil it contains: 180 liters, which we convert to cubic meters (180 × 0.001 m³/liter).
The weight of the diesel can be found by multiplying its volume by its density (∙ 830 kg/m³) and by the acceleration due to gravity (g ≈ 9.81 m/s²) to get its weight in newtons. Adding this to the weight of the drum yields the total weight of the drum and oil.
The buoyant force provided by the sea water, which has a typical density of about 1025 kg/m³, will equal this total weight when the drum is floating. By equating the weight of the fluid displaced (Volume of sea water displaced × density of sea water × g) to the total weight of the drum and diesel, we can solve for the volume of sea water displaced. Knowing the radius of the drum, we can translate this volume back into a height to represent the submerged depth or draught.
Through these calculations, we would find the correct answer, which is 55 cm (Option c).