Acylindrical hole is drilled in a sphere x² + y² + z² = a² to make a bead. the hole is such that the center of the hole is drilled symmetrically through the center of the sphere. the width of the hole is determined so that when a string of length 2l (l > a) is passed through the hole, at least the half of the string remains out side the bead. what is the minimum width (diameter) of the hole that would allow this?