Question

Scurrilous con artists have been known to represent gold-plated tungsten ingots as pure gold and sell them to the greedy at prices much below gold value but deservedly far above the cost of tungsten. With what accuracy must you be able to measure the mass of such an ingot in and out of water to tell that it is almost pure tungsten rather than pure gold?

Short answer

It helps in differentiating between the gold and tungsten very easily.

Step-by-step solution

Conceptual Introduction

Fluid statics, often known as hydrostatics, is a branch of fluid mechanics that investigates the state of balance of a floating and submerged body, as well as the pressure in a fluid, or imposed by a fluid, on an immersed body.

Mass of gold and tungsten

The ratio of the object's density to the density of the fluid in which it is immersed determines the fraction submerged in the fluid.

Let’s assume that we have$1ml$of sample.

If it is tungsten than it will have density of tungsten is $19.30g/mL$.

Hence the mass of the tungsten will be:

$$\begin{gathered} {\rho }_t=\frac{m_t}{V_t} \\ 19.30=\frac{m_t}{1} \\ {m}_t=19.30\text{g} \end{gathered}$$

The mass of$1mL$tungsten is$19.30g$.

Let’s assume that we have$1mL$of gold

If it is tungsten than it will have density of gold is $19.32g/mL$.

Hence the mass of the gold will be:

$$\begin{gathered} {\rho }_g=\frac{m_g}{V_g} \\ 19.32=\frac{m_g}{1} \\ {m}_g=19.32g \end{gathered}$$

The mass of 1 ml of gold is 19.32 g.

Where the uncertainty should lie?

The answer should be at least in the thousand’s places; the scale measure should be to the thousands.

Therefore, it can help in differentiating between the gold and tungsten easily.