Does the density of an object depend on its size

How would you place two electrons on a sphere of radius r so that the electrostatic potential energy is minimized. how would you place three electrons to solve the same problem.

An open cart is moving along a straight frictionless horizontal track. when rain starts falling vertically into the cart, what happens to the speed of the cart?

Asap and show ! a 14 kg rock starting from rest free falls through a distance of 5.0 m with no air resistance. find the momentum change of the rock caused by its fall and the resulting change in the magnitude of earths velocity. earth mass is 6.0 * 10^24 kg. show your work assuming the rock earth system is closed.