A student makes a special flat shape out of a flat sheet of metal. It consists of a central square that has a mass

M and a side of length L$.$ A smaller square made out of the same type of metal sheet but with a side of L$/2$is

attached to one corner. Another smaller square with a side of L$/4$ is attached to the second square, and so on$,$

until the squares are the size of an atom. Six of these are shown below, but the pattern goes on for a long time.

$($a$)$ Estimate the total diagonal length of this creation.

$($b$)$ What is the total mass?

$($c$)$ Find the location of the center of mass.