Question

A jeweller claims that he sells ornaments made of pure gold that has the relative density of 19.3. He sold a bangle weighing 25.25 gf to a person. The clever customer weighs that bangle when immersed in pure water and finds that it weighs 23.075 gf in water. Is the ornament made by pure gold?

Answer 1

It states that a body immersed in a fluid is buoyed up by a force equal to the weight of the displaced fluid.

Now let us examine the given situation. The mass of the ornament as stated by the jeweller is $25.25g$ and the density is $19.3gm/cc$

Now on immersing the ornament in water, the mass in water is $23.075g$. We know the volume of water displaced by the substance when we immerse it in water is equal to the volume of the substance.

We know that density of water is $1gm/cc$

Also here the difference in the mass of the substance in air to that in water is,$=25.25-23.075=2.175g$. This is the mass of the displaced water.

Also we know that

$Density=\frac{Mass}{Volume}$

Mass of displaced water$=2.175g$

Density$=1gm/cc$

Hence, volume of the water displaced$=2.175cc$

This should be equal to the volume of the ornament.

Now, let us calculate the density of the ornament.

Mass$=25.25g$

Volume$=2.175cc$

Density$=\frac{25.25}{2.175}=11.58gm/cc$

But the jeweller stated that density of the gold is $19.3gm/cc$.

Hence we will say that gold is not pure.