ASPX authentication cookie issue in virtual directory

I have 3 applications running at my end.

1. RootSite
2. RootSite/VirtualDirectory1
3. RootSite/VirtualDirectory2

I have a 开发者_开发技巧login page in three of these applications. When I login in either of these applications the .ASPXAUTH cookie is set but I am seeing that all of the three applications are updating the same .ASPXAUTH cookie instead of creating individual one. For example a user login on "RootSite", .ASPXAUTH cookie is created, now the user comes and login in the application "RootSite/VirtualDirectory1" and this time I am seeing the same .ASPXAUTH cookie is updating. I am confirming this because the created date of this cookie has been changed. So this means instead of creating a new cookie it is using the same cookie. How can I resolve this ? I don't want to interfere the logged-in logged-out status of one application with the other ?

Add\Change the name attribute in your Forms Authentication web config entry - See this article