Question

A solid box made from a material whose density is rhoS floats with two thirds of its volume submerged in a liquid whose density is rhoL. How do the two densities compare?

Answer 1

Answer:

$\frac{\rho_S}{\rho_L} = \frac{2}{3}$

Explanation:

density of the solid box material = $\rho_s$

density of the liquid material = $\rho_L$

Given that

solid box floats with two thirds of its volume submerged in a liquid

let V be the volume of the box

then,

$V\rho_sg= \frac{2V}{3}\rho_L g$

⇒$\frac{\rho_S}{\rho_L} = \frac{2}{3}$

so, the ratio of densities of solid and and the liquid is 2/3