Mathematical and Physical Journal
for High Schools
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# Problem P. 4238. (March 2010)

P. 4238. A thin-walled plexy cylinder of mass M and of radius R can rotate freely without friction about its horizontal axis. Inside there is a solid rubber cylinder of mass m and of radius r. What is the period of the motion of the system when the rubber cylinder is displaced a little from its equilibrium position? It can be assumed that the rubber cylinder rolls without sliding inside the plexy one.

(5 pont)

Deadline expired on April 12, 2010.

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

Megoldás. $\displaystyle T=2\pi\sqrt{\frac{3M+m}{2M+m}\frac{R-r}{g}}$

### Statistics:

 21 students sent a solution. 5 points: Béres Bertold, Galzó Ákos Ferenc, Jéhn Zoltán, Lájer Márton, Neumer Tamás, Pálovics Péter, Patartics Bálint. 4 points: Laczkó Zoltán Balázs, Szabó 928 Attila, Vuchetich Bálint. 3 points: 2 students. 2 points: 1 student. 1 point: 8 students.

Problems in Physics of KöMaL, March 2010