Question

Take the density of the crown to be rho_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 rho_c and the density of water rho_w. Imagine that the apparent weight of the crown in water is W_apparent = 4.50 N, and the actual weight is W_actual = 5.00 N. Is the crown made of pure (100%) gold? The density of water is rho_w = 1.00 grams per cubic centimeter. The density of gold is rho_g = 19.32 grams per cubic centimeter. Yes No

Answer 1

Part A) We know that $W = \rho Vg$

Actaual weight of crown   $W_{actual} = \rho_{c} Vg$

Apprant weight of crown = Actual weight of crown - water displaced

$W_{apparent} = \rho_{c} Vg- \rho _{w}Vg$

$\frac{W_{apparent}}{W_{actual}} = \frac{\rho_{c} Vg- \rho _{w}Vg}{\rho_{c} Vg}= 1-\frac{\rho _{w}}{\rho _{c}}$

Part B

$\frac{W_{apparent}}{W_{actual}} =\frac{4.5}{5}= 1-\frac{\rho _{w}}{\rho _{c}}$

$\frac{\rho _{w}}{\rho _{c}}= 1- \frac{4.5}{5} = 0.1$

$\rho _{c}= \frac{\rho _{w}}{0.1} = \frac{1/ccg}{0.1} = 10 g/cc$

As $\rho _{c}< \rho _{gold}$   so crown is not made of pure gold.