1. A goblet consists of a uniform thin hemispherical cup of radius r, a circular base of the same material thickness and radius as the cup, and an intervening stem of length r and whose weight one quarter of that of the cup. (a) Show that the height of the centre of gravity above the base is (13/14)r. (b) If the mass of the goblet is M and that of the amount of liquid that fills it is M' . Show that filling it raises the centre of gravity through a distance (39/65) r (M'/M+M') 2. X = x1M1 + x2M2+....xnMn / M1+M2+....Mn where x is the centre of mass of each body that makes up the goblet and M is their respective mass 3. I've managed to do part a where I've considered the surface densities of the hemispherical shell, the rectangular stem and since it's from the base, I considered the mass off the circle but the distance to the base would be 0. So C.O.M of the hemispherical shell = r/2 + r (from the start till the base) C.O.M of the stem is r/2 to the base C.O.M circle = 0 since it's to the base itself Then Mass = surface density x area ; surface density is represented by sigma Area of hemisphere = 2 pi r^2 so m= 2 pi r^2 (sigma) Area of circle = pi r^2 so m = pi r^2 (sigma) And m of stem = 1/4 (mass of hemisphere) = pi r ^2 /2 Plug it into the equation and you get 13/14 r What I don't get is part b since they haven't mentioned whether how full the cup is? How do we find its centre of mass?