Problem P. 4762. (October 2015)
P. 4762. A piece of iron is attached to the bottom of a wooden cylinder of cross section \(\displaystyle A_0\), so the wooden cylinder is floating in a sample of liquid of density \(\displaystyle \varrho_1\), which liquid is in a beaker of cross-section \(\displaystyle A_1\). The beaker is also floating in some liquid of density \(\displaystyle \varrho_2\), in another bigger beaker of cross section \(\displaystyle A_2>A_1\). This beaker is also floating in some liquid of density \(\displaystyle \varrho_3\) in another even wider beaker of cross-section \(\displaystyle A_3>A_2\), and so on...\(\displaystyle \,\). Altogether there are \(\displaystyle n\) beakers on the table. The symmetry axes of all beakers and the wooden cylinder are vertical.
Then the wooden cylinder is pushed down by a vertical force of \(\displaystyle F\). (Neither the wooden cylinder nor any of the beakers touch the other beaker below them.)
\(\displaystyle a)\) By what amount did the height of immersed part of the wooden cylinder in the first liquid increase?
\(\displaystyle b)\) By what amount did the level of the liquid in the first liquid increase?
\(\displaystyle c)\) By what amount did the level of the liquid in the \(\displaystyle i\)-th beaker increased?
Deadline expired on November 10, 2015.
69 students sent a solution. 5 points: Asztalos Bogdán, Balogh Menyhért, Blum Balázs, Büki Máté, Csorba Benjámin, Édes Lili, Fekete Balázs Attila, Forrai Botond, Gémes Antal, Gergely 444 Kornél, Iván Balázs, Jakus Balázs István, Juhász 326 Dániel, Kádár 012 István, Kasza Bence, Korecz Gábor, Kormányos Hanna Rebeka, Kovács Péter Tamás, Körmöczi Dávid, Mány Bence, Németh 777 Róbert, Németh Ciprián, Olosz Adél, Pszota Máté, Sal Kristóf, Sallai Krisztina, Szántó Benedek, Szentivánszki Soma , Tófalusi Ádám, Tomcsányi Gergely, Tompa Tamás Lajos, Tóth Adrián, Vitay Olivér. 4 points: Di Giovanni András, Kiss Antónia Véda, Radnai Bálint. 3 points: 5 students. 2 points: 10 students. 1 point: 11 students. 0 point: 6 students. Unfair, not evaluated: 1 solution.