The gravitational self potential energy of a solid ball of mass density ρ and radius r is e. what is the gravitational self potential energy of a ball of mass density ρ and radius 2r in terms of e?

Consider an insulating crystal, made up of layers of atoms. what form would you expect the temperature dependence of the phonon heat capacity to approach at extremely low temperatures if the interlayer coupling is i)very strong (rigid coupling), and ii) very weak. explain.