Mathematical and Physical Journal
for High Schools
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# Problem P. 4711. (February 2015)

P. 4711. Six alike simple pendulums are made of electrically insulating threads of negligible mass and of small metal spheres of mass 5 g. The length of each pendulum is 0.5 m. The six pendulums are hung at the same point, and then they are all rotated about a vertical axis through this point. After a long enough time each small sphere revolves along a circular path of radius $\displaystyle r$ in a horizontal plane.

$\displaystyle a)$ What is the radius $\displaystyle r$ of the path, if the period of the motion is 1 s?

$\displaystyle b)$ What same amount of charge should be added to the spheres in order that they stay at the circumference of the same radius of circle $\displaystyle r$, without rotation?

(4 pont)

Deadline expired on March 10, 2015.

### Statistics:

 53 students sent a solution. 4 points: Asztalos Bogdán, Balogh Menyhért, Bekes Nándor, Blum Balázs, Büki Máté, Csathó Botond, Csorba Benjámin, Fehér Balázs, Fekete Balázs Attila, Fekete Panna, Forrai Botond, Holczer András, Iván Balázs, Jakus Balázs István, Juhász 326 Dániel, Kasó Ferenc, Körtefái Dóra, Lőrincz Zoltán, Mándoki László, Marosvári Kristóf, Németh Flóra Boróka, Nenezic Patrick Uros, Olosz Balázs, Páhoki Tamás, Pázmán Előd, Rózsa Tibor, Sal Kristóf, Szántó Benedek, Szász Norbert Csaba, Szentivánszki Soma , Tóth Bence Tamás, Varju Ákos, Wesniczky Albert, Wiandt Péter, Zöllner András. 3 points: Bencsik Bálint, Berta Dénes, Di Giovanni Márk, Erdei Ákos, Fehér 169 Szilveszter, Kalmár Bendegúz, Koch Lilla, Kormányos Hanna Rebeka, Marozsák Tóbiás , Szilágyi Kristóf, Varga-Umbrich Eszter. 2 points: 4 students. 1 point: 3 students.

Problems in Physics of KöMaL, February 2015