(Solved): 1. A homogeneous hemisphere of weight W and radius a rests on a perfectly smooth horizontal table a ...

1. A homogeneous hemisphere of weight $W$ and radius a rests on a perfectly smooth horizontal table as shown. One edge at $D$ is tied to a point $B$ on the table by means of a light inextensible string of length $b(b<a)$. The center of mass $C$ is $3/8$ a from $O$. Find the tension in the string in terms of $W$, $a$, and $b$.