Final answer:
To find the inner and outer radii of the hollow spherical shell that just barely floats in water, we need to use Archimedes' principle. By equating the weight of the shell to the buoyant force, we can solve for the radius of the shell. The inner radius is smaller than the outer radius, and the inner radius is the radius of the hollow space between the inner and outer surfaces of the shell.
Step-by-step explanation:
To find the inner and outer radii of the hollow spherical shell, we need to use Archimedes' principle. Archimedes' principle states that the buoyant force on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.
In this case, the shell is barely floating in water, which means the buoyant force equals the weight of the shell. The weight of the shell can be calculated by multiplying its mass by the acceleration due to gravity.
The density of the shell is given as 2.60 x 10³ kg/m³. By dividing the mass of the shell by its volume, we can find the average density. The volume of the shell can be calculated using the formula for the volume of a sphere.
By equating the weight of the shell to the buoyant force, we can solve for the radius of the shell. The inner radius is smaller than the outer radius. Therefore, the inner radius is the radius of the hollow space between the inner and outer surfaces of the shell.
Considering the given information, the inner radius of the shell is _ m and the outer radius is _ m.