Answer:
[tex]\dfrac{5}{8}[/tex]
Explanation:
m = Mass of object = [tex]\rho v[/tex]
m' = Mass of water = [tex]\rho' v'[/tex]
[tex]\rho[/tex] = Density of object
[tex]\rho'[/tex] = Density of water
Weight of the water displaced is the force in the case of floating objects
According to the question
[tex]v'=\dfrac{5}{8}v[/tex]
In the case of floating objects
[tex]W=W'\\\Rightarrow mg=m'g\\\Rightarrow \rho vg=\rho'v'g\\\Rightarrow \rho v=\rho' \dfrac{5}{8}vg\\\Rightarrow \rho=\rho' \dfrac{5}{8}\\\Rightarrow \dfrac{\rho}{\rho'}=\dfrac{5}{8}[/tex]
The ratio of the density of the object to that of water is [tex]\dfrac{5}{8}[/tex]
