A hollow spherical body with inner and outer radii of 6 cm and 8 cm respectively floats half-submerged in water. Determine the density of the material of the sphere.

Step-by-step solution

Let the density of the material of the sphere be . Inner radius of the hollow sphere, r = 6 cm . Outer radius of the hollow sphere, R = 8 cm . Volume of the material of the hollow sphere is given by V = 4 3 (R^3 - r^3) . Weight of the hollow sphere is W = V g = 4 3 (R^3 - r^3) g . Since the sphere floats half-submerged in water, the volume of water displaced is half of the total volume of the sphere. Volume of displaced water, V_d = 1 2 4 3 R^3 . Buoyant force exerted by water is F_B = V_d _w g = 1 2 4 3 R^3 _w g ,