A dangling modifier is a type of a modifier which is placed incorrectly or the noun it is supposed to modify isn't clearly stated in the sentence.
Having this in mind, the sentence which contains a dangling modifier is <span>A. Playing with the children, it was obvious they had a good time.
It should be rewritten somehow to say: It was obvious they had a good time playing with the children. </span>
<span> Curie, a two-time Nobel Prize recipient and physics professor at the Sorbonne (a college of the University of Paris), presented this speech at Vassar College in Housekeeping, New York, on May 14, 1921. The speech, preserved in print as no. 2 of Vassar's Ellen S. Richards Monographs series, centers on what Curie called "the somewhat peculiar conditions of the discovery of radium" and her view that "the scientific history of radium is beautiful." The speech is provided online at the Gifts of Speech Web site, by Liz Linton, site director; and electronic resources and serials librarian in Cochran Library, Sweet Briar College, Virginia.</span>
Rite of passage, I'm pretty sure