electrostatics - Does charge of a metal charged by induction determine by which ends of the metal is grounded to?

Does charge of a metal charged by induction determine by which part of the metal is ground to? I draw a diagram to make it simple to understand:

Right diagram: When ground is touched with the positive side of the metal, electrons flow to the negative and the metal become negatively charged.

Left diagram: When ground is touched with the negative side of the metal, electrons flow to the ground and the metal become positively charged.

Is this true? Because opposite charges repel.