Question

A crown weighs 66.0-lb when in air and 60.5-lb when in water. The crown is made of gold and silver. Given that the densities of gold and silver are 19,300 kg/m?³? and 10,500 kg/m?³?, (a) Determine the volume of the crown. (b) Calculate the mass percentage of gold and silver in the crown.

Answer 1

(a)

1 lb =0.453 kg

so, 66 lb = 29.93 kg

and 60.5 lb = 27.44 kg

when it is immersed in water then buoyancy force = density of water * volume of water displaced * g

here the buoyancy force is equal to (m_2 -m_1)*g

= (29.93 - 27.44)*g

=2.49 *g

so, 2.49 *g = 997* volume displaced * g

volume displaced = 0.00249 m^3

(b)

density = Mass / volume

So, Mass = density * volume

let the percentage of gold is 100 - X then the percentage of silver is X

Now Mass = 29.93 = {Mass_1 *(100 - X) + Mass_2 * X}/100

29.93 = {density_1 *(100 - X) + density_2 * X}* 0.00249/100

12020.08 = 193 * (100 - X) + 105 * X

88 * X = 7279.92

X = 82.72

silver mass percentage = 82.72 and gold mass percentage = 17.28

X =