Question

A king ordered a goldsmith to prepare a crown with $1\mathrm{kg}$pure gold. the relative density of pure gold is given as$\text{'}19\text{'}$It is possible to find the adulteration if the goldsmith adds some impurity in making the crown. If so how? Explain.

Answer 1

Step 1:- Given Data

$$\begin{gathered} \mathrm{Mass}\mathrm{of}\mathrm{crown}\left({\mathrm{m}}_{\mathrm{g}}\right)=1\mathrm{kg} \\ \mathrm{Relative}\mathrm{density}(\mathrm{R}.\mathrm{D}.)=19 \end{gathered}$$

Step 2: On calculating the density of the pure gold

$$\begin{gathered} \mathrm{R}.\mathrm{D}=\frac{\mathrm{density}\mathrm{of}\mathrm{gold}\left({\mathrm{\rho }}_{\mathrm{g}}\right)}{\mathrm{density}\mathrm{of}\mathrm{water}\left({\mathrm{\rho }}_{\mathrm{w}}\right)} \\ 19=\frac{{\mathrm{\rho }}_{\mathrm{g}}}{1000}...(\because {\mathrm{\rho }}_{\mathrm{w}}=1000\raisebox{1ex}{$\mathrm{kg}$}\!\left/ \!\raisebox{-1ex}{${\mathrm{m}}^3$}\right.) \end{gathered}$$

So,$$\begin{gathered} {\mathrm{\rho }}_{\mathrm{g}}=19\times 1000 \\ =19000\raisebox{1ex}{$\mathrm{kg}$}\!\left/ \!\raisebox{-1ex}{${\mathrm{m}}^3$}\right. \end{gathered}$$

Hence, If the goldsmith adds some adulteration as an impurity in making the crown, then the density of the adulterated gold will change.
Since we already calculate the density of the pure gold is $19000\raisebox{1ex}{$\mathrm{kg}$}\!\left/ \!\raisebox{-1ex}{${\mathrm{m}}^3$}\right.$, So we can easily justify the adulteration.