By signing in you confirm you are 18 or older, or have your parent’s or guardian’s consent.

NDA 2 2024 GAT, question 64

Topic: Physics

Q64

Shown in the figure are two hollow cubes C1C_{1} and C2C_{2} of negligible mass partially filled (depicted by darkened area) with liquids of densities ρ1\rho_{1} and ρ2\rho_{2}, respectively, floating in water (density ρW\rho_{W}). The relationship between ρ1,ρ2\rho_{1},\rho_{2} and ρW\rho_{W} is

Figure for Q64

  1. (a) ρ2<ρW<ρ1\rho_{2}<\rho_{W}<\rho_{1}
  2. (b) ρ2<ρ1<ρW\rho_{2}<\rho_{1}<\rho_{W}
  3. (c) ρ1<ρ2<ρW\rho_{1}<\rho_{2}<\rho_{W}
  4. (d) ρ1<ρW<ρ2\rho_{1}<\rho_{W}<\rho_{2}Correct answer

Solution.

Answer: (d) ρ1<ρW<ρ2\rho_{1}<\rho_{W}<\rho_{2}

  1. For each negligible-mass cube, floating equilibrium gives ρliquid A hliquid=ρwater A hsubmerged.
  2. In C₁ the internal liquid column is higher than the submerged depth, so ρ₁<ρW.
  3. In C₂ it is lower, so ρ₂>ρW.
  4. Together, ρ₁<ρW<ρ₂.