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An object weighing 297 N in air is immersedin water after being tied to a string connectedto a balance. The scale now reads 263 N.Immersed in oil, the object appears to weigh270 N.Find the density of the object.Answer in units of kg/m^3Do not round.

Sagot :

Given

Wair = 297 N

Wwater = 263 N

Density of water = 1000 kg/m^3

Acceleration due to gravity = 9.8

Procedure

We can calculate the thrust of the water with the difference of weights

[tex]\begin{gathered} W_{\text{air}}-W_{\text{water}}=\rho_wgV \\ V=\frac{W_{\text{air}}-W_{\text{water}}}{\rho_wg} \\ V=\frac{297N-263N}{1000\cdot9.8} \\ V=0.00347\text{ m}^3 \end{gathered}[/tex]

Now for the object

[tex]\begin{gathered} \rho_{\text{obj}}=\frac{W_{\text{air}}}{gV} \\ \rho_{\text{obj}}=\frac{297}{9.8\cdot0.00347} \\ \rho_{\text{obj}}=8735.29kg/m^3 \end{gathered}[/tex]

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