(a) When the positively charged rod is brought near sphere A, it induces a separation of charges in the metallic spheres A and B due to electrostatic induction.
Initially, when the rod is brought close to sphere A, electrons in sphere A (since it's a conductor) will be repelled by the positive charge on the rod and move away from the rod's vicinity, leaving a net positive charge on sphere A. At the same time, due to the repulsion of electrons in sphere A, electrons in sphere B will be attracted towards sphere A, leading to an accumulation of negative charge on the side of sphere B facing sphere A.
So, after separation, sphere A will have a net positive charge, and sphere B will have a net negative charge.
(b) The metallic balls are supported on insulated stands to prevent the charges on the spheres from neutralizing or redistributing due to grounding. If the spheres were not supported on insulated stands and were in contact with a conducting surface (ground), any excess charge on the spheres would flow into the ground, equalizing the charges and neutralizing the system. This would make it difficult to demonstrate or observe the charge separation induced by the charged rod.
By using insulated stands, the spheres are effectively isolated from any external conducting surfaces. This prevents the excess charges from escaping to the ground, allowing the induced charge separation to be maintained and observed for educational purposes or experiments involving electrostatics.