You must compute the ratio of the actual weight of the crown (W_actual) and the apparent weight of the crown when it is submerged in water (W_apparent). See whether you can follow in Archimedes' footsteps. The figure in the attached file shows what is meant by weighing the crown while it is submerged in water.
Take the density of the crown to be p_c. What is the ratio of the crown's apparent weight (in water), W_apparent, to its actual weight, W_actual?
Express your answer in terms of the density of the crown (p_c) and the density of water (p_w).
