Track / Stage 5 / 49 of 400 #649 of 2000

Problem 649

AIME late

Algebra Difficulty 5.1 Find the answer

1.2. With what minimum force must a cube with a volume of $10 \mathrm{~cm}^{3}$ , floating in water, be pressed so that it is completely submerged? The density of the material of the cube is 500 kg/ $\mathbf{m}^{3}$ , the density of water is $1000 \mathrm{kg} / \mathrm{m}^{3}$ . Give the answer in SI units. The acceleration due to gravity is taken to be $10 \mathrm{~m} / \mathrm{s}^{2}$ .

Your answer

Official solution

1.2. What is the minimum force required to press a cube with a volume of $10 \mathrm{~cm}^{3}$ , floating in water, so that it is completely submerged? The density of the cube material is 500 kg/ $\mathbf{m}^{3}$ , and the density of water is $1000 \mathrm{kg} / \mathrm{m}^{3}$ . Provide the answer in SI units. The acceleration due to gravity is taken as $10 \mathrm{~m} / \mathrm{s}^{2}$ .

Answer. 0.05 .

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.