2. Consider a thin rectangular slab of uniform material (perhaps a thin metal plate) of thickness \(t\), length \(l\) and width \(w\)
\(l\)
\(w\)
\(t\)
The volume of this slab is \(V = lwt\), the mass is \(M = \rho lwt\) where \(\rho\) is the uniform density of the slab.
Use the definition of center of mass:
\(X_{cm} = \frac{1}{M} \iiint x\rho \,dx\,dy\,dz\)
with similar definitions for \(Y_{cm}\) and \(Z_{cm}\). Show that the center of mass of this plate is at
\(X_{cm} = l/2\), \(Y_{cm} = w/2\) and \(Z_{cm} = t/2\)