Question

A goldsmith desires to test the purity of a gold ornament suspected to be mixed with copper.The ornament weighs 0.25 kg in air and is observed to displace 0.015 litre of water when immersed in it. Densities of gold and copper with respect to water are, respectively, 19.3 and 8.9.The approximate percentage of copper in the ornament is?

Answer 1

Hint : Purity of gold can be found by using Archimedes Principle an object immersed in a fluid experiences a buoyant force that is equal in magnitude to the force of gravity on the displaced fluid, that is the force generated on an object is equal to the weight of the fluid displaced by the object


Complete step by step solution:
$
  {\text{In air weight of ornament = 0}}{\text{.25 kg}}
  {\text{Volume in water when the ornament immersed in it}}
   \Rightarrow {\text{V = 0}}{\text{.015 litre}}
   \Rightarrow {\text{ V = 0}}{\text{.015 }}{{\text{m}}^3}
  {\text{Density of gold and copper with respect to water are }}
  {\text{19}}{\text{.3 and 8}}{\text{.9 respectively}}{\text{.}}
  {\text{Now, as per the question }}
  {\text{Let eight of copper = x kg}}
   \Rightarrow {\text{Weight of gold = (0}}{\text{.25 - x)}}
  {\text{Now, }}\frac{x}{{19.3}}{\text{ + }}\frac{{0.25 - x}}{{8.9}}{\text{ = 0}}{\text{.015}}
  {\text{or, 0}}{\text{.0518 x + 0}}{\text{.1123 (0}}{\text{.25 - x) = 0}}{\text{.015}}
   \Rightarrow - {\text{ 0}}{\text{.0605 x = - 0}}{\text{.01308}}
   \Rightarrow x{\text{ = 0}}{\text{.216}}
  {\text{percentage of copper in the ornament = }}\frac{{0.216}}{{0.25}}{\text{ }} \times {\text{ 100}}
  \therefore {\text{percentage of copper in the ornament = 86}}{\text{.4\% }}
 $

Additional Information: Archimedes' theory states that an upward force that is exerted on a body immersed in a fluid, whether fully or partially submerged, is equal to the weight of the body's displaced fluid.
Archimedes used the principle of purchase to ascertain the purity of gold. Accordingly, a body immersed in a fluid experiences a purchasing force equal to the weight of the fluid it displaces. With the help of this theory, the density of the golden crown and the density of the solid gold were compared by balancing the crown on a scale with a reference piece, the set is then immersed in water. If the crown is less dense than gold, it will displace more water, and it will experience more force than the reference piece.

Note: Buoyancy is the force that causes objects to float. It is a force exerted on an object that is partially or completely immersed in a fluid. Buoyancy occurs due to the difference in pressure acting on the opposite sides of an object submerged in static fluid. It is also known as Buoyant Force. Example A submarine has a large ballast tank, which is used to control its position and depth from the ocean surface. A submarine sinks water by pouring it into a ballast tank so that its weight exceeds the buoyant force.