Chapter 19, Problem 56A

A prospector desires to know if a nugget is pure gold. The nugget has a mass of 380 grams on a balance. When immersed in water its mass appears as 350 grams. Is the nugget pure gold?

To determine

To identify: If the nugget is pure gold or not.

Answer to Problem 56A

The nugget is not pure gold.

Explanation of Solution

Given:

Mass of nugget on a balance, $m_{\text{air}}=380\text{g}$

Mass of nugget if immersed in water, $m_{\text{water}}=350\text{g}$

Formula Used:

The density is given as,

  $\rho =\frac{m}{V}$

Where $m$ is mass and $V$ is volume.

Calculation:

According to Archimedes principle, the buoyancy force is equal to difference of mass of object in air and water that is,

  $\begin{array}{l}{F}_{\text{buoyancy}}=380\text{ g}-350\text{g}\\ \text{=30}\text{g}\end{array}$

Also this mass is equal to volume of displaced liquid.

So, volume of water displaced is 30 cm³.

Now, density of nugget

  $\begin{array}{l}{\rho }_{\text{nugget}}=\frac{m}{V}\\ =\frac{380\text{g}}{30{\text{cm}}^3}=12.6{\text{g/cm}}^3\end{array}$

But, ${\rho }_{\text{gold}}=19.3{\text{g/cm}}^3$

It means nugget is not pure gold.

Conclusion:

Therefore, the nugget is not pure gold.