According to legend, the following challenge led Archimedes to thediscovery of his famous principle: Hieron, king of Syracuse, wassuspicious that a new crown that he had received from the royalgoldsmith was not pure gold, as claimed. Archimedes was ordered todetermine whether the crown was in fact made of pure gold, with thecondition that only a nondestructive test would be allowed. Rather thananswer the problem in the politically most expedient way (or perhapsextract a bribe from the goldsmith). Archimedes thought about theproblem scientifically. The legend relates that when Archimedes steppedinto his bath and caused it to overflow, he realized that he could answerthe challenge by comparing the volume of water displaced by the crownwith the volume of water displaced by an amount of pure gold equal inweight to the crown. If the crown was made of pure gold, the two volumeswould be equal. If some other (less dense) metal had been substituted forsome of the gold, then the crown would displace more water than thepure gold.A similar method of answering the challenge, based on the same physicalprinciple, is to compute the ratio of the actual weight of the crown,Wactual, and the apparent weight of the crown when it is submerged inwater, WWapparent. See whether you can follow in Archimedes' footsteps.The figure shows what is meant by weighing the crown while it issubmerged in water.(Figure 1)FigureII< 1 of 1>Part ATake the density of the crown to be pc. What is the ratio of the crown's apparent weight (in water) Wapparent to its actual weight Wactual?Express your answer in terms of the density of the crown pc and the density of water pw.▸ View Available Hint(s)WapparentsWactualSubmit6,2Temptates Symbols undo reço reset keyboard shortcuts help31Previous AnswersX Incorrect; Try Again; 4 attempts remainingProvide FeedbackPart B Complete previous part(s)

Name: According to legend, the following challenge led Archimedes to thedis
Uploaded: 2024-03-20T06:51:10.000Z
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Description: According to legend, the following challenge led Archimedes to thediscovery of his famous principle: Hieron, king of Syracuse, wassuspicious that a new crown that he had received from the royalgoldsmith was not pure gold, as claimed. Archimedes was