A machine part is made up of two pieces, with centers of gravity shown in the figure.$($Figure $1)$

Figure$1$ of $1$

A machine part is made up of two pieces. Piece $1$ is a rectangle with the center of gravity at its center. The second piece is an L$-$shaped block with the shorter leg being vertical, and the longer leg extending horizontally rightward from the upper end of the shorter leg. Its center of gravity is located to the right of and below its interior right angle and to the right of and above the lower end of its vertical leg. The lower end of the vertical leg of piece $2$ is connected to the right part of the top surface of piece $1.$ The pieces are comparable in size. Point A is located above the center of gravity of piece $1,$ slightly below and to the left of the center of gravity of piece $2,$ and to the left of piece $2.$ Point B is located above and slightly to the right of the center of gravity of piece $2,$ inside the horizontal leg of piece $2.$ Point C is located to the left of the center of gravity of piece $1,$ below and slightly to the right of the center of gravity of piece $2,$ outside of both pieces. Point D is located above and to the right of the center of gravity of piece $1,$ below and to the left of the center of gravity of piece $2,$ and at the connection of piece $1$ and piece $2.$

Part A

Which point could be the center of gravity of the entire part?

A

B

C

D