Final answer:
With the data provided, we cannot accurately determine the specific weight of the sphere since it requires knowledge of the sphere's actual weight in air, not just the tension in the mooring line. Thus, the correct option for the specific weight in kN/m^3, from the choices given, cannot be identified without additional information.
Step-by-step explanation:
To determine the specific weight of the sphere immersed in seawater, we can use the concept of buoyancy and Archimedes' principle. The specific weight (weight per unit volume) can be found using the formula for the buoyant force, which is the tension of the mooring line plus the weight of the sphere. Given that the sphere radius is 38 cm (0.38 m), we can calculate the volume of the sphere using the formula V = (4/3)πr^3.
The volume of the sphere is V = (4/3)π(0.38 m)^3 = 0.2309 m^3. Since the tension of the mooring line (which is the upward force required to keep the sphere submerged) is 710 N, we can find the weight of the sphere in water by adding this tension to the gravitational force acting on the sphere. Assuming that g (the acceleration due to gravity) is 9.8 m/s^2, we find the weight of the sphere as Weight = Volume × Specific Weight = 0.2309 m^3 × Specific Weight.
To find the specific weight, we rearrange the equation: Specific Weight = (Tension + Weight) / Volume. Here we need to take into account the weight of the object is countered by the buoyancy force so the tension in the mooring line is actually equal to the difference in the weight of the sphere in air and the buoyant force. Without the actual weight of the sphere, there isn't enough information to calculate the specific weight. Therefore, we cannot determine the specific weight with the information provided, and thus cannot find the correct option between a) 7.015 kN/m^3, b) 0.710 kN/m^3, c) 1.903 kN/m^3, and d) 9.800 kN/m^3.