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:

• A. ${\left(4M/3\rho \right)}^2/3$
• B. ${\left(M/3\rho \right)}^2/3$
• C. ${\left(M/4\rho \right)}^2/3$
• D. None of these

Answer 1

Answer: (D)

None of these

According to law of floatation, weight of cube = weight of liquid displaced
$\Rightarrow Mg=\frac{3}{4}{l}^3\rho g\Rightarrow l^3=\frac{4M}{3\rho }\Rightarrow l={\left(\frac{4M}{3\rho }\right)}^{\frac{1}{3}}$