Find potential of a ball inside a grounded shell

[tigigi]

I have this question that initially a metal ball of radius r1 with potential v1, then surrounded by a conducting shell with radius r2. Find potential of ball if shell grounded.

So v1 =kq/r1, then q=vr1/k, can I say directly that shell will have -q since it's induced by ball?
Then v ball will be kq /r1 + k(-q)/r2 ?
I'm not sure if I find should count the potential due to shell when I find the v ball?
Thanks for help.

 

[mfb]

Looks correct.

I'm not sure if I find should count the potential due to shell when I find the v ball?

You'll need that, or the condition that the shell has a potential of zero. Both approaches are possible and looks very similar.