Question

An object floats in water with 5 8 of its volume submerged. The ratio of the density of the object to that of water is

Answer 1

Answer:

$\dfrac{5}{8}$

Explanation:

m = Mass of object = $\rho v$

m' = Mass of water = $\rho' v'$

$\rho$ = Density of object

$\rho'$ = Density of water

Weight of the water displaced is the force in the case of floating objects

According to the question

$v'=\dfrac{5}{8}v$

In the case of floating objects

$W=W'\\\Rightarrow mg=m'g\\\Rightarrow \rho vg=\rho'v'g\\\Rightarrow \rho v=\rho' \dfrac{5}{8}vg\\\Rightarrow \rho=\rho' \dfrac{5}{8}\\\Rightarrow \dfrac{\rho}{\rho'}=\dfrac{5}{8}$

The ratio of the density of the object to that of water is $\dfrac{5}{8}$