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A cubical block floats in a liquid with exactly half its volume submerged. The whole system (liquid plus block) is then accelerated upward with an acceleration g/3. What fraction of the block's volume is now submerged?

1. 1/2
2. 3/8
3. 2/3
4. 3/4

Correct answer: 1/2

Solution

Floating equilibrium under upward acceleration a: buoyant force minus weight = (mass)*a. With effective gravity g_eff = g + a, both rho_liquid*V_sub*g_eff (buoyancy) and rho_block*V*g_eff (weight) scale identically. The fraction f = V_sub/V = rho_block/rho_liquid is independent of g_eff, so it stays at 1/2.

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