Question

A jeweller claims that he makes the ornament of pure gold that has a relative density of $19.3$. He sells a bangle weighing $25.25gf$ to a person. The clever customer weighs the bangle when immersed in water and finds that it weighs $23.075gf$ in water. With the help of suitable calculations find out whether the ornament is made of pure gold or not.

• A. Pure gold
• B. Not pure gold
• C. cant say
• D. none

Answer 1

The correct option is B Not pure gold

We will solve this problem using Archimedes principle.

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 jeweler is $25.25g$ and the density is $19.3g/cc$.

Now on immersing the ornament in water, the mass in water is $23.07g$. We know that 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 $1g/cc$.

Also, here the difference in the mass of the substance in air to that in water is 25,25 - 23.07 = 2.18 g. This the mass of the displaced water.

Also, we know that $Density=Mass/Volume$.

So, Mass of displaced water = $2.18g$.

Density = $1g/cc$.

Hence, the volume of the water displaced is $2.18cc$.

This should be equal to the volume of the ornament. Now, let us calculate the density of the ornament.

Mass = $25.25g$, Volume = $2.18cc$ and Density = $\frac{25.25}{2.18}=11.58g/cc$

But the jeweler stated that the density of gold is $19.3g/cc$.

Hence, we will say that the gold is not pure.