A large platform is balanced on a triangular wedge about its center. Two spheres of equal and homogeneous density $($such that their masses are proportional to their volumes$)$ are placed on opposite sides of the platform. The larger sphere, with a radius of $2$ meters, is placed $2$ meters away from the pivot point. Where could the smaller sphere, of radius $1$ meter, be placed as to keep the platform level? $($Assume that the spheres have a flat enough base as to prevent them from rolling.$)$