Let o be the mass density of a (negligibly thick) distribution of mass over a surface S. That is, is the mass per unit area at each point on S; it may vary over S. Then the x, y, coordinates of the center of gravity are defined as where Ic 31 Vc = 24 11 !! M 1) M M = xo dA, yo dA, zo dA. = 11 od dA (1.1) (11.2) is the total mass. Evaluate ze in each case. (You need not evaluate ye. e) (a) S is the plane surface = 2 + 2y with vertices at (0,0,0). (1.0, 1), (0.1.2);= constant = dg. (b) S is the plane surface == x+y with vertices at (0,0,0). (1,0, 1), (0.1, 1); o = 1 + y. 2 = 0 and 2 = 1.= constant = do th) S is the spherical surface a2 + 1/ (c) S is the plane surface z = (0.1.2). (2.0.0). (2. 1.0): 2-z with vertices at (0, 0, 2). 4-*. (d) S is the plane surface == 2-zwith vertices at (0,0, 2). (0, 1, 2). (2,0,0);=i+r. S is the cylindrical surface a + y = 4 between == 0 and == h.o=1+r. (1)S is the cylindrical surface + y = 4 between = = 0 and 2=2+0= constant dg. (g) is the hemispherical surface a + y + 2 = 1 between