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).

Transcribed Image Text:

n2 imi 2 n t m