Potential/Charge on Concentric Conducting Shells

[blgeo]

I'm not 100% confident in my reasoning for this question because my answer seems unlikely:

Homework Statement

A spherical capacitor comprises two thin metal spheres of different radii but with
a common centre. The following series of operations is completed: The spheres are mutually connected by an internal wire. The outer sphere is raised to potential +V with respect to ground. The internal connection is broken. The outer sphere is returned to ground potential. Determine the final potential and the final charge on the inner sphere.

Homework Equations

Gauss' Law (integral form)

The Attempt at a Solution

As the spheres are connected by a wire initially I assume when the outer sphere is raised to V the inner sphere must be too. As they are at the same potential I think the charge on the inner sphere must be 0 at this point so that there is no field between the spheres (Gauss). When the connection is broken the inner sphere must then retain 0 net charge, and so when the outer sphere is returned to ground potential i think the inner sphere must have no charge and be at 0V with respect to ground.

This is the best argument I could come up with but I'm struggling to convince myself! Any help/confirmation of this answer would be appreciated

 

[sunjin09]

It sounds reasonable to me

 

[rude man]

You can stop struggling now ...