Final answer:
To find the tension in the cord when a 1.2-kg metal sphere is immersed in water, we use the concept of buoyant force. The volume of the sphere is first calculated and then used to determine the buoyant force by considering the water displaced. The tension is then the difference between the weight of the sphere and the buoyant force, which is approximately 7.056 N.
Step-by-step explanation:
The student has asked to find the tension in the cord when a 1.2-kg solid sphere made of a metal with density of 2500 kg/m³ is immersed in water. To find the tension, we can use the concept of buoyant force, which is equal to the weight of the water displaced by the sphere. The density of water is 1000 kg/m³.
First, we calculate the volume of the sphere using its mass (m) and density (d) with the formula V = m/d. The sphere's volume, V, is 1.2 kg / 2500 kg/m³ = 0.00048 m³. The weight of the water displaced is then calculated using the volume of the sphere and the density of water. The buoyant force (Fb) then is 0.00048 m³ × 1000 kg/m³ × 9.8 m/s² (acceleration due to gravity) equaling approximately 4.704 N.
The tension in the cord (T) is equal to the weight of the sphere minus the buoyant force. The weight of the sphere (W) is its mass multiplied by the acceleration due to gravity, W = 1.2 kg × 9.8 m/s² = 11.76 N. Therefore, the tension is T = W - Fb = 11.76 N - 4.704 N ≈ 7.056 N.
So the tension in the cord when the sphere is immersed in water is closest to 7.056 N.