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Imagine that the apparent weight of the crown in water is [tex]W_{apparent}[/tex] = 4.50N, and the actual weight is [tex]W_{actual}[/tex] = 5.00N. Is the crown made of pure (100%) gold?
The density of water is [tex]\rho_w[/tex] = 1.00 grams per cubic centimeter. The density of gold is [tex]\rho_g[/tex] = 19.32 grams per cubic centimeter.

Respuesta :

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

Explanation :

Formula used :

[tex]\frac{W_{apparent}}{W_{actual}}=1-\frac{\rho_w}{\rho_c}[/tex]

where,

[tex]W_{apparent}[/tex] = apparent weight of the crown in water = 4.50 N

[tex]W_{actual}[/tex] = actual weight = 5.00 N

[tex]\rho_w[/tex] = density of water = [tex]1.00g/cm^3[/tex]

[tex]\rho_c[/tex] = density of crown = ?

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

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

[tex]\rho_c=10g/cm^3[/tex]

Density of crown < Density of gold

[tex]10g/cm^3<19.32g/cm^3[/tex]

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

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