Final answer:
To calculate the volume of the submerged object, use the difference between the actual weight and the apparent weight to find the buoyant force, then divide by the product of the density of water and gravitational acceleration. The object's volume is found to be 0.0644 m³.
Step-by-step explanation:
The question asks for the volume of a 90 kg object submerged in water given that its apparent weight is 250 N. To find the volume, we use the principle of buoyancy, where the buoyant force is equal to the weight of the water displaced by the object. Since the object is submerged, the buoyant force is also the difference between the actual weight in air (gravitational force) and the apparent weight in water.
The formula to calculate the buoyant force (B) is B = weight_in_air - apparent_weight_in_water. First, we find the actual weight in air by multiplying the mass by the acceleration due to gravity (g = 9.81 m/s2). Weight_in_air = mass × g = 90 kg × 9.81 m/s2 = 882 N. The buoyant force is then 882 N - 250 N = 632 N.
To find the volume of the water displaced (which is the same as the object's volume), we use the relation ship between the buoyant force and the volume displaced: B = ρ_water × V × g, where ρ_water is the density of water (approximately 1000 kg/m3). We rearrange the equation to solve for V: V = B / (ρ_water × g). Plugging in the numbers, we get V = 632 N / (1000 kg/m3 × 9.81 m/s2) = 0.0644 m3.