b. If the mass distribution of a solid object does not allow a simple determination of the center of mass by symmetry, the following expressions must be used:

[tex]\frac{1}{m} *\int\limits {x} \, dm[/tex]

[tex]\frac{1}{m} *\int\limits {y} \, dm[/tex]

[tex]\frac{1}{m} *\int\limits {z} \, dm[/tex]

Where x, y and z are the coordinates of a small fragment of the solid with mass m. Use the above expressions to calculate the x, y, and z coordinates of the center of mass of a plate with uniform density ( ρ) as shown in the figure. The mass of the plate is:



M=[tex]\frac{1}{2}* p*b*h*t[/tex]