Answer
The x-coordinate of the center of mass is $21.2~cm$
Work Step by Step
We can find the x-coordinate of the center of mass of each of the three objects:
sphere:
mass: $200 ~g$
center of mass: $x = 5~cm$
cylinder:
mass: $450 ~g$
center of mass: $x = 18.5~cm$
rectangular solid:
mass: $325 ~g$
center of mass: $x = 35~cm$
We can find the x-coordinate of the center of mass:
$x_{com} = \frac{(200~g)(5~cm)+(450~g)(18.5~cm)+(325~g)(35~cm)}{200~g+450~g+325~g}$
$x_{com} = \frac{20,700~g~cm}{975~g}$
$x_{com} = 21.2~cm$
The x-coordinate of the center of mass is $21.2~cm$
