In order to solve the problem it is necessary to take into account the concepts related to the moment of inertia, and the center of mass of the object.
Our values are given by:
m = 0.514kg
I = 4.7m (each side)
A) For the case when the axis passes through the midpoints of opposite sidesand lies in the plane of the square. The formula is given by,
[tex]I = 4m (\frac{l}{2})^2\\I = 4*(0.514)(\frac{4.7}{2})^2\\I = 11.35kgm^2\\[/tex]
B) For the case when the axis passes through the midpoint of one of the sides and is perpendicular to the plane of the square. The formula is given by,
[tex]I = 2m(\frac{l}{2})^2+2m(\frac{l}{2}^2+l^2)\\I = 2*(0.514)*(\frac{4.7}{2})^2+2*(0.514)*((\frac{4.7}{2})^2+4.7^2)\\I = 34.06Kgm^2[/tex]
C) For the case when the axis lies in the plane of square f passes through two diagonally opposite particles,
[tex]I = \frac{1}{2}*l^2[/tex]
[tex]I = \frac{1}{2}*(4.7)^2[/tex]
[tex]I = 11.045kgm^2[/tex]
