Answer:
[tex]V=2.026*10^4cm^3[/tex]
[tex]\rho=2.03\frac{g}{cm^3}[/tex]
Explanation:
By the Archimedes principle we know that every body submerged in a fluid is buoyed up by a force equal to the weight of the fluid displaced by the object.
Due to this, the object has a loss weight when immersed in alcohol of:
[tex]403N-264N=139N[/tex]
So, we can find the displaced mass of alcohol:
[tex]m=\frac{W}{g}\\m=\frac{139N}{9.8\frac{m}{s^2}}\\m=14.18kg[/tex]
Now, we calculate the displaced volume of alcohol, which is the same volume of the object:
[tex]V=\frac{m}{\rho}\\V=\frac{14.18*10^3g}{0.7\frac{g}{cm^3}}\\V=2.026*10^4cm^3[/tex]
Object mass is:
[tex]m=\frac{W}{g}\\m=\frac{403N}{9.8}=41.12kg[/tex]
Finally, we can find the density of the object:
[tex]\rho=\frac{m}{V}\\\rho=\frac{41.12*10^3g}{2.025*10^4cm^3}\\\rho=2.03\frac{g}{cm^3}[/tex]
