Final answer:
The volume of the man with a mass of 80 kg and a density of 955 kg/m³ is approximately 0.0838 m³, corresponding to option (a). The buoyant force air exerts on him is approximately 0.9995 N. The ratio of the buoyant force to his weight is about 0.127%.
Step-by-step explanation:
To calculate the volume of a man with a mass of 80 kg and a density of 955 kg/m³, we use the formula for density: density = mass/volume. By rearranging this formula to solve for volume, we get volume = mass/density. Plugging in the man's mass and the provided density gives us:
volume = 80 kg / 955 kg/m³ = 0.0838 m³ (approximately)
Therefore, the correct answer is (a) 0.083 m³. Now, let's find the buoyant force air exerts on him. The buoyant force on an object in air can be calculated using the weight of the air displaced by the object. Since air has a density at sea level of about 1.225 kg/m³, the weight of the air displaced is equal to the density of air times the gravitational acceleration times the volume of the man:
buoyant force = density of air × gravitational acceleration × volume
buoyant force = 1.225 kg/m³ × 9.81 m/s² × 0.0838 m³ = approximately 0.9995 N
To find the ratio of the buoyant force to his weight, we first calculate his weight, which is mass times the gravitational acceleration:
weight = mass × gravitational acceleration
weight = 80 kg × 9.81 m/s² = 784.8 N
Then, we divide the buoyant force by his weight:
ratio = buoyant force / weight
ratio = 0.9995 N / 784.8 N = approximately 0.00127 (or 0.127%)