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<R, 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 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.