Jonas Salk, an American physician whose careful studies demonstrated a means of providing lasting immunity to polio.
(A) Jonas Salk, an American physician whose careful studies demonstrated a means of providing lasting immunity to polio.
Jonas Salk - Subject is without a verb; whose - relative pronoun starts a relative clause having careful subjects as subject and demonstrated as verb.
Fragment - Incorrect
(B) Providing lasting immunity to polio was demonstrated by Jonas Salk, an American physician with careful studies.
Providing...., - Modifier; an American... -> Subject without a verb
Fragment - Incorrect(C) Jonas Salk was an American physician who had careful studies which demonstrated a means of providing lasting immunity to polio.
Clause, relative pronoun; had careful studies - distortion in meaning, trying to imply as if studies weren't his but may be developed by someone else and he just happened to have them. - Incorrect
(D) Jonas Salk was an American physician whose careful studies demonstrated a means of providing lasting immunity to polio.
Correct; Good sentence structure(E) Jonas Salk, whose careful studies demonstrated a means of providing lasting immunity to polio, an American physician.
Subject, Modifier, Modifier - No verb to the main subject - Fragment - Incorrect