Question

Imagine that the apparent weight of the crown in water is
`W_(apparent)` = 4.50N, and the actual weight is
`W_(actual)` = 5.00N. Is the crown made of pure (100%) gold?

The density of water is
`\rho_w` = 1.00 grams per cubic centimeter. The density of gold is
`\rho_g` = 19.32 grams per cubic centimeter.

Answer 1

Answer : The crown is not made of pure (100%) gold.

Explanation :

Formula used :

`(W_(apparent))/(W_(actual))=1-(\rho_w)/(\rho_c)`

where,

`W_(apparent)` = apparent weight of the crown in water = 4.50 N

`W_(actual)` = actual weight = 5.00 N

`\rho_w` = density of water =
`1.00g/cm^3`

`\rho_c` = density of crown = ?

Now put all the given values in the above formula, we get:

`(4.50N)/(5.00N)=1-(1.00g/cm^3)/(\rho_c)`

`\rho_c=10g/cm^3`

Density of crown < Density of gold

`10g/cm^3<19.32g/cm^3`

Thus, the crown is not made of pure (100%) gold.