#### Problem 6P

Archimedes Principle states that the buoyant force on an object partially or fully submerged in a fluid is equal to the weight of the fluid that the object displaces. Thus, for an object of density 0 floating partly submerged in a fluid of density f, the buoyant force is given by F=fgh0A(y)dy, where g is the acceleration due to gravity and A(y) is the area of a typical cross-section of the object see the figure. The weight of the object is given by W=0ghLhA(y)dy a Show that the percentage of the volume of the object above the surface of the liquid is 100f0f b The density of ice is 917 kg/m3 and the density of seawater is 1030 kg/m3. What percentage of the volume of an iceberg is above water? c An ice cube floats in a glass filled to the brim with water. Does the water overflow when the ice melts? d A sphere of radius 0.4 m and having negligible weight is floating in a large freshwater lake. How much work is required to completely submerge the sphere? The density of the water is 1000 kg/m3.