Question

Imagine that the apparent weight of the crown in water is itle="W_{apparent}" alt="W_{apparent}" align="absmiddle" class="latex-formula"> = 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 :

$\frac{W_{apparent}}{W_{actual}}=1-\frac{\rho_w}{\rho_c}$

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:

$\frac{4.50N}{5.00N}=1-\frac{1.00g/cm^3}{\rho_c}$

$\rho_c=10g/cm^3$

Density of crown < Density of gold

$10g/cm^3$

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