IDNLearn.com is designed to help you find accurate answers with ease. Our platform is designed to provide trustworthy and thorough answers to any questions you may have.
Sagot :
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].
Thank you for using this platform to share and learn. Don't hesitate to keep asking and answering. We value every contribution you make. Your questions find clarity at IDNLearn.com. Thanks for stopping by, and come back for more dependable solutions.
