The app is free, but does show advertisements. Combining ads with streaming around 50MB per cartoon makes for a power-hungry application. While it's worth bearing that in mind, it's by no means a reason to not try the application. There are 161 episodes on offer, which will keep you and the kids occupied for plenty of time.
My only concern is that the app may disappear if there is a copyright infringement complaint from MGM. I'm not entirely sure whether Tom and Jerry are still copyrighted. Either way, enjoy these classics while you can, and introduce your kids to them.