Mathematical and Physical Journal
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# Problem P. 4523. (March 2013)

P. 4523. Five alike =0.5 metre long pendulums are made of electrically insulating threads and of small metal spheres of mass m=50 milligram. Each small sphere is given the same type of electrical charge of Q=10-7 coulomb, and the pendulums are hung at the same point. Reaching the equilibrium position, because the mutual repulsion the small spheres will be on the circumference of a horizontal circle.

a) What is the radius of this circle?

b) What would the number of revolution of the rotation of the pendulums be, if they were to rotate about a vertical axis going through the point at which they are hung, and the small spheres were to move along the circumference of the above described circle such that the spheres had no charge on them?

(5 pont)

Deadline expired on April 10, 2013.

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

Megoldásvázlat. $\displaystyle a)$ 41 cm.

$\displaystyle b)$ $\displaystyle \omega=5{,}9~\rm s^{-1}$; $\displaystyle f=1{,}06~$fordulat/s.

### Statistics:

 63 students sent a solution. 5 points: Antalicz Balázs, Bingler Arnold, Büki Máté, Csathó Botond, Fekete Panna, Kaprinai Balázs, Kovács 444 Áron, Kovács-Deák Máté, Körei Réka Enikő, Medek Ákos, Olosz Balázs, Reitz Angéla, Sal Kristóf, Sárvári Péter, Seress Dániel, Szirbik Bence, Trócsányi Péter, Vajda Balázs, Váli Tamás, Varju Ákos. 4 points: Balogh Menyhért, Berczi Benjámin, Buttinger Milán, Czipó Bence, Dinev Georgi, Emri Tamás, Fehér Zsombor, Fonyó Viktória, Garai Zoltán, Garami Anna, Holczer András, Janzer Barnabás, Kacz Dániel, Kollarics Sándor, Nagy Gergely, Papp Roland, Szabó 928 Attila, Szilágyi 585 Dezső, Szilágyi András, Tatár Dániel, Tuhári Richárd, Virágh Anna, Zsiros Ádám. 3 points: 9 students. 2 points: 8 students. 1 point: 2 students. 0 point: 1 student.

Problems in Physics of KöMaL, March 2013