Problem P. 3839. (November 2005)
P. 3839. A small test tube is placed into a high cylinder which is nearly totally filled with water. The test tube is placed upside down into the water, and in its top a certain amount of air remains, such that the test tube floats. The cylinder is closed by a piece of thin rubber. If the rubber is pressed, the test tube descends and if the excess pressure on the rubber is ceased the test tube ascends. But it comes up only if it did not go below the depth of 2 m. Find the height of the that part of the test tube which was above the water before the cylinder was closed by the piece of rubber. (The mass of the cylinder-shaped test tube is 0.5 g, its inner cross section is 0.5 cm2, and its length is 5 cm. The density of water is 1000 kg/m3, the density of glass is 2500 kg/m3, and the external pressure is 105 Pa.)
Deadline expired on December 12, 2005.
56 students sent a solution. 5 points: Csirmaz Dávid, Engedy Balázs, Farkas Ádám László, Kocsis Vilmos, Kónya 495 Gábor, Máté István Mátyás, Molnár 811 Kristóf, Nagy 317 Péter, Nyíri Dávid Ákos, Pásztor Attila, Pósa László, Szabó 001 Áron, Széchenyi Gábor, Szolnoki Lénárd, Szük Dániel, Tóth 123 László, Török Balázs, Tüzes Dániel, Vécsi Áron, Werner Miklós. 4 points: Blázsik Zoltán, Dudás János, Hotzi Bernadette, Kruppa Gergő, Mándi Gábor, Matulik Gábor, Nagy 555 Zoltán, Remes Kristóf Bence, Sinkó József, Székely Gergely, Szilágyi Zsombor, Takács 484 Marcell, Takátsy Balázs, Tűri Balázs. 3 points: 17 students. 1 point: 1 student. 0 point: 1 student. Unfair, not evaluated: 3 solutions.