A piece of copper immersed in water has an apparent weight of 2.65 N and when it is immersed in a liquid of density 1.50 x 103 kg/m3 its apparent weight is 2.50 N.

Question

Is it pure copper or does it contain any other metal?

Copper density 8.9 X 103 kg/m3.

Answer 1

As the density of copper is greater than either fluid, the piece of copper is totally immersed. The net force on the copper in water is mg - V_Cu x d_H2O x g = 2.65, where m is the mass of the copper. The net force in the second fluid is mg - V_Cu x d_fluid x g = 2.50. Solving each equation for mg and equating the results gives 2.65 + V_Cu x d_H2O x g = 2.50 + V_Cu x d_fluid x g. This can be rearranged and solved for V_Cu to give 0.15/(g(d_fluid - d_H2O)) = 3.06 x 10^-5 mm³. This value of V_Cu is substituted into the first equation given and solved for mass which gives 3.01 x10^-1 kg. The density can then be calculated to give 9.84 x 10³ kg/m³. This result indicates that the copper is not pure.