I developed a dynamic web project in Eclipse. I can access the app through my browser using the following URL:
http://localhost:8080/MyDynamicWebApp
Setting the path to nothing in the Eclipse web modules edit dialog enabled me to access the project without any path component in the URL (i.e. ROOT)
You can reach the web modules edit dialog by pressing F3 if you select Tomcat in the "Servers" view or by double clicking on it.
Some screenshots: