Final answer:
The powerful female performer with a voice like coarse sandpaper is Janis Joplin, a legendary figure in rock history.
Step-by-step explanation:
The performer who is often described as having a voice like coarse sandpaper and who became the most powerful female performer of the rock era, while expressing the agony of a sad and hopeless life, is a) Janis Joplin. Known for her raw and emotional performances, Janis Joplin's music reflected her intense and troubled life, making her a legendary figure in rock and roll history.