Final answer:
To calculate the magnitude of the apparent weight of the ball, you can use the formula weight = mass * acceleration due to gravity. By calculating the weight of the ball and the weight of the fluid it displaces, you can find the apparent weight. In this case, the magnitude of the apparent weight of the ball is 15 N.
Step-by-step explanation:
To calculate the magnitude of the apparent weight of the ball, we need to first calculate the weight of the ball and then subtract the weight of the fluid it displaces. The weight of an object can be calculated using the formula: weight = mass * acceleration due to gravity. The acceleration due to gravity is approximately 9.8 m/s^2.
The mass of the ball can be calculated using the formula: mass = density * volume. Plugging in the given values, we find that the mass of the ball is 0.930 g/cm³ * 15000 cm³ = 13950 g = 13.95 kg.
The weight of the ball is therefore: weight = mass * acceleration due to gravity = 13.95 kg * 9.8 m/s² = 137.01 N.
Next, we calculate the weight of the fluid displaced by the ball using the same formula. The density of the fluid is given as 0.830 g/cm³. The volume of the fluid displaced is equal to the volume of the ball, which is 15000 cm³.
The mass of the fluid is: mass = density * volume = 0.830 g/cm³ * 15000 cm³ = 12450 g = 12.45 kg.
The weight of the fluid is: weight = mass * acceleration due to gravity = 12.45 kg * 9.8 m/s² = 122.01 N.
Finally, the magnitude of the apparent weight of the ball can be calculated as the difference between the weight of the ball and the weight of the fluid: apparent weight = weight of the ball - weight of the fluid = 137.01 N - 122.01 N = 15 N.