The weight of a king's solid crown is w. When the crown is suspended by a light rope and completely immersed in water, the tension in the rope (the crown’s apparent weight) is fw.
(a) Prove that the "crown's relative density (specific gravity) is 1 / (1 - f). Discuss the meaning of the limits as f approaches 0 and 1.
(b) If the crown is solid gold and weighs 12.9 N in air, what is its apparent weight when completely immersed in water?
(c) Repeat part (b) if that Own is solid lead with very thin gold plating, but still has a weight in air of 12.9 N.