Suppose that the left sphere in Figure 10 has density k and the right sphere density ck. Find the y-coordinate of the center of mass of this two-sphere solid (convince yourself that the analogue of Problem 33 of Section 13.5 is valid).

Let S1 and S2 be disjoint laminas in the xy-plane of mass m1 and m2 with centers of mass (xÌ…1, yÌ…1) and (xÌ…2, yÌ…2). Show that the center of mass (xÌ…, yÌ…) of the combined lamina S1 ( S2 satisfies

with a similar formula for yÌ…. Conclude that in finding (xÌ…, yÌ…) the two laminas can be treated as if they were point masses at (xÌ…1, yÌ…1) and (xÌ…2, yÌ…2).

n2 imi 2 n t m