Two solid spheres of radius Rand mass m are initially separated by a distance d such that the two centres of mass are separated by d+2R as shown below. The spheres are initially at rest, but the gravitational force accelerates them towards each other until they collide. d+2R R R d a) Calculate the initial mechanical energy of the system. [1 mark] b) Calculate the gravitational potential energy of the system at the moment they collide, taking v to be the velocity (for either object) at the moment of the collision. [2 marks] c) Derive an expression for v. State carefully what physical law you are applying. [4 marks] d) Show that, in the limit d>> R, the velocity v is independent of d. [3 marks)