A solid sphere with a radius of 5 cm floats in water. If a maximum load of 0.1 kg can be placed on it without getting the load wet, determine the specific gravity of the sphere's material.

Step-by-step solution

Let the volume of the sphere be V and the density of its material be _s . Volume of the sphere is given by: V = 4 3 R^3 Substituting R = 5 cm : V = 4 3 (5)^3 = 500 3 cm ^3 When the maximum load is placed on the sphere without getting wet, the sphere is completely submerged in water. By Archimedes' principle, the buoyant force equals the total weight of the sphere and the load. V _w g = (M + m) g V _w = V _s + m Given the mass of the load m = 0.1 kg = 100 g and the density of water _w = 1 g/cm ^3 : 500 3 (1) = 500 3