Mathematical and Physical Journal
for High Schools
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# Problem P. 4425. (March 2012)

P. 4425. A small object is mounted to the perimeter of a hoop of radius r. The mass of the object and the hoop is the same. The hoop is placed into a fixed semi-cylinder shaped rough trough of radius R, such that the small mass is at the top. Find the least r/R ratio such that the equilibrium state of the hoop is stable.

(6 pont)

Deadline expired on April 10, 2012.

Sorry, the solution is available only in Hungarian. Google translation

Megoldás. $\displaystyle \frac{r}{R}> \frac{1}{3}$ esetén stabil az egyensúly.

### Statistics:

 41 students sent a solution. 6 points: Beke Gabriella, Bolgár Dániel, Fehér Zsombor, Fonyó Viktória, Garami Anna, Horicsányi Attila, Iglói Gábor, Janzer Olivér, Juhász Péter, Kabos Eszter, Koncz Gabriella, Kovács 444 Áron, Mázik László, Medek Ákos, Nagy Lajos, Papp Roland, Park Choong Eun, Sárvári Péter, Szabó 928 Attila, Szélig Áron, Trócsányi Péter, Ürge László, Vajda Balázs. 4 points: 5 students. 3 points: 7 students. 2 points: 1 student. 0 point: 5 students.

Problems in Physics of KöMaL, March 2012