# Physics Cup – TalTech 2023 – Problem 1

By Jaan Kalda (TalTech).

A solid cylinder of radius $R$ and height $H$ has density $\rho_c$ and is immersed in water of density $\rho_w$. The cylinder is initially kept at rest so that its axis is vertical, and the distance between its bottom face and the bottom of the water container is $h$. The water container has a flat rigid bottom, and the depth of water in it is larger than $H+h$. At a certain moment, the cylinder is released and starts falling. How long it will take for the cylinder to hit the bottom? Neglect viscosity. Assume that $\rho_c>\rho_w$, $H, and $10\rho_ch\ll \rho_wR$.

Chinese translation of problem 1 (下沉的圆柱)

Please submit the solution of this problem via e-mail to physcs.cup@gmail.com. First intermediate results will be published on 20th November, 13:00 GMT. First hints will appear here on 27th November 2022, 13:00 GMT. After the publication of the first hint, the base score is reduced to 0.9 pts. For full regulations, see the “Participate” tab.