Problem 2.3 Center of mass of a paraboloid

A paraboloid emerges by rotating a parabola about its symmetry axis, see Figure 2.21. Con- sider the homogeneous paraboloid consisting - Vab of (x, y, z) E R' satisfying x2 + y 0. Determine its volume. Use symmetry arguments to con- clude that the center of mass lies on the z-axis. Figure 2.21: Paraboloid. Compute the location of the center of mass.Consider a system of two objects of masses m1 and 111;, respectively. Show that the locations of these objects can be recovered from the center of mass R and the relative position F as