Two cubes A and B of same dimensions are made of different materials with densities $\rho_{\mathrm{A}}$ and $\rho_{\mathrm{B}}$, respectively. Cube A floats in water with a fraction $\eta$ of its volume immersed. When cube B is placed on top of cube A , it is found that cube $A$ is just entirely immersed, while cube $B$ is entirely above the surface of the water. What is the ratio $\rho_{\mathrm{B}} / \rho_{\mathrm{A}}$ ?

• Correct answer
  A

  $(1-\eta) / \eta$
• B

  $\eta$
• C

  $1 / \eta$
• D

  $\eta /(1-\eta)$

Hence, the correct answer is option: 'A'.