In my opinion, relativistic mass is useful in general only in the context defined by these 7 assumption:
speed of light is isotropic only in one inertial frame (that we can call absolute space, presumably anchored to cosmic masses).
when an object is in absolute motion, its dimensions are...
Unluckily no, I can't expand now my assertion, I'm too busy and I studied this subject time ago (and I don't plain to study it again in the immediate future). Simply I remember that I found this section decidedly not clear as the rest of the book (and I taken heart by Griffiths comment "If you...
(preamble: I'm sorry for the english but I'm not mother tongue)
Griffiths is a very good book. It is true that once authors taken seriously their job (think to Born books or to delicious old Dover) while today we are submerged by always new books of little quality, but Griffiths books are rare...