Consider a galaxy modelled as the region between the two infinite, parallel planes z = R and z = + R in Cartesian coordinates. The mass density is uniform inside the galaxy, p(x,y, z) = py for =R R Making physically plausible assumptions for the gravitational field, solve this equation to find V(z) and the force per unit mass /' = dV/dz inside and outside the galaxy. Show that F(z) does not vanish as [z| oo, and give a brief physical explanation for why this is the case. A particle is released from rest at z = R. Prove that it undergoes simple harmonic motion and obtain an expression for how long it takes to return to its original position