Question

The words longing and melancholy both have meanings that imply sadness. Which word with a similar meaning would an author use to convey a sense of yearning?

Answer 1

The answer that would convey yearning would be longing. It wouldn't be melancholy pretty much means sad. 

Longing ex: She was longing for one of her grandmother's hugs.

Answer 2

longing, cause yearning means like crying for someone. longing also means the same thing kinda like wailing.