Problem 1 – Hint 3

Let $x$ be the height of the cylinder from the bottom of the vessel; you should obtain an expression for the kinetic energy in the form $T=a\frac {\dot x^2}x$, where $\dot x=\frac {\mathrm dx}{\mathrm dt}$, and $a$ is a constant. Now there are two ways to proceed. First, you can express $\mathrm dt$ from the energy conservation law $T+K=E_0$ in terms of $\mathrm dx$ and integrate. Second and mathematically simpler way is to substitute $x=\xi^2$ to obtain a nice equation for $\ddot \xi$.

Please submit the solution to this problem via e-mail to physcs.cup@gmail.com. The next hint for the Problem 1 will be published alongside with the Problem No 2 at 13:00 GMT, 18th December 2022, together with the next updates of the intermediate results.