Question

A uniform cube of mass M is floating on the surface of a liquid with three fourth of its volume immersed in the liquid(density $=\rho$). The length of the side of the cube is equal to?

Answer 1

Given mass of the cube = M and volume =V.

Condition-$\frac{3}{4}$ V is submerged in the fluid of density $\rho$.

Let the density of cube be ${\rho }_C$

We know ,

Weight of the cube=weight of the fluid displaced

${\rho }_{C}gV=\frac{3}{4}V\rho g$

${\rho }_c=\frac{3}{4}\rho$

Also Density$=\frac{Mass}{Volume}=>{\rho }_c=\frac{M}{a^3}{a}^3=\frac{4M}{3\rho }a=\sqrt[3]{3\frac{4M}{3\rho }}$