In: Physics

Imagine that the apparent weight of the crown in water is \(W_{\text {apparent }}=4.50 \mathrm{~N},\) and the actua weight is \(W_{\text {actual }}=5.00 \mathrm{~N}\). Is the crown made of pure \((100 \%)\) gold? The density of water is \(\rho_{\mathrm{w}}=1.00\) grams per cubic centimeter. The density of gold is \(\rho_{\mathrm{g}}=19.32\) grams per cubic centimeter.

- Yes
- No

$$ \begin{aligned} &\frac{W_{a p p a r e n t}}{W_{a c t u a l}}=\frac{4.5}{5}=1-\frac{\rho_{w}}{\rho_{c}}\\ &\frac{\rho_{w}}{\rho_{c}}=1-\frac{4.5}{5}=0.1\\ &\rho_{c}=\frac{\rho_{w}}{0.1}=\frac{1 / c c g}{0.1}=10 g / c c\\ &\text { As } \rho_{c}<\rho_{\text {gold}} \text { so crown is not made of pure gold. } \end{aligned} $$

The crown is not made of pure gold.

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