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Answer: The mass density is 1166.36 [tex]kg/m^{3}[/tex].
Explanation:
Given: Weight of sample in air [tex](F_{air})[/tex] = 500 N
Weight of sample in alcohol [tex](F_{alc})[/tex] = 200 N
Specific gravity = 0.7 = [tex]0.7 \times 1000 = 700 kg/m^{3}[/tex]
Formula used to calculate Buoyant force is as follows.
[tex]F_{B} = F_{air} - F_{alc}\\= 500 - 200 \\= 300 N[/tex]
Hence, volume of the material is calculated as follows.
[tex]V = \frac{F_{B}}{\rho \times g}[/tex]
where,
[tex]F_{B}[/tex] = Buoyant force
[tex]\rho[/tex] = specific gravity
g = acceleration due to gravity = 9.81
Substitute the values into above formula.
[tex]V = \frac{F_{B}}{\rho \times g}\\= \frac{300}{700 \times 9.81}\\= \frac{300}{6867}\\= 0.0437 m^{3}[/tex]
Now, mass of the material is calculated as follows.
[tex]mass = \frac{F_{air}}{g}\\= \frac{500 N}{9.81}\\= 50.97 kg[/tex]
Therefore, density of the material or mass density is as follows.
[tex]Density = \frac{mass}{volume}\\= \frac{50.97 kg}{0.0437 m^{3}}\\= 1166.36 kg/m^{3}[/tex]
Thus, we can conclude that the mass density is 1166.36 [tex]kg/m^{3}[/tex].
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