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# Problem P. 4257. (May 2010)

P. 4257. In a hollow hemisphere a thin ring rolls down without slipping, starting from one endpoint of one of the horizontal diameters. At what speed does it reach the bottom point of the sphere? The radius of the ring is r=2 cm and the radius of the hemisphere is n=4 times as much as that of the ring. The hemisphere is fixed and the plane of its cross section is horizontal.

(4 pont)

Deadline expired on June 10, 2010.

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

Megoldás. $\displaystyle v=\sqrt{g(n-1)r}\approx0,\!77$ m/s.

### Statistics:

 77 students sent a solution. 4 points: Balogh Gábor, Batki Bálint, Bay Dorottya, Béres Bertold, Bodosi Eszter, Bolgár Dániel, Burján Bence, Csizmadia Luca, Csuka Róbert, Czigány Máté Gábor, Farkas Martin, Filep Gábor, Fonai Dániel, Galzó Ákos Ferenc, Hoksza Zsolt, Horváth Dániel, Juhász 214 Dániel, Kaposvári István, Kollarics Sándor, Kovács 444 Áron, Kozma Bálint, Kulcsár Flóra, Kungl Ákos Ferenc, Kunsági-Máté Sándor, Laczkó Zoltán Balázs, Lájer Márton, Láng Hanga, Mayer Martin János, Molnár Alexandra, Nagy László Bendegúz, Pálovics Péter, Para Attila, Patartics Bálint, Pázmán Koppány, Péterffy Gábor, Pető János, Pinczei Emese, Pirka Benjámin Zoltán, Rácz Viktor, Rácz Viktória, Sisák Mária Anna, Szabó 928 Attila, Szélig Áron, Szentgyörgyi 994 Rita, Szigeti Bertalan György, Szikszai Lőrinc, Takács 737 Gábor, Tamási Mátyás, Varju 105 Tamás, Vuchetich Bálint. 3 points: 22 students. 2 points: 2 students. 1 point: 2 students. 0 point: 1 student.

Problems in Physics of KöMaL, May 2010