Let G be the center of gravity of a uniform solid rectangular parallelepiped with sides 2a, a, a.Find the moments of inertia of the parallelepiped about a system of rectangular axes through G and parallel to the sides of the parallelepiped.

Question

Can anyone please explain how to calculate the center of gravity of a parallelepiped?
Thanks!

Answer 1

Clearly G is the geometric center of the solid, since it is of uniform density.
the center of a line is the midpoint, right?
center of a rectangle is where the diagonals intersect.
same for a brick -- halfway along each dimension.