Mathematical and Physical Journal
for High Schools
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# Problem P. 4251. (April 2010)

P. 4251. Two alike pendulums of length L are suspended at the same point. At the end of both pendulums there are small spheres of mass m. If both spheres are given the same Q charge, the threads move apart as it is shown in the figure.

a) Determine the mass m of the spheres.

b) In another experiment the sphere on the right is changed to another one of the same charge, but three times bigger mass. How should the charge of the left sphere be changed, so that in equilibrium the distance between the two spheres remains L? (The mass of the left sphere is not changed.)

(5 pont)

Deadline expired on May 10, 2010.

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

Megoldás. $\displaystyle a)$ $\displaystyle m=\frac{\sqrt{3}kQ^2}{gL^2}$;

$\displaystyle b)$ $\displaystyle Q'=\sqrt{\frac{27}{13}}Q$

### Statistics:

 77 students sent a solution. 5 points: Balogh Gábor, Batki Bálint, Benyó Krisztián, Béres Bertold, Bolgár Dániel, Filep Gábor, Fonai Dániel, Fülep Andrea , Galzó Ákos Ferenc, Hartstein Máté, Hegedűs Csaba, Janosov Milán, Jéhn Zoltán, Kaposvári István, Koncz Gabriella, Kovács 444 Áron, Kovács Attila, Kungl Ákos Ferenc, Laczkó Zoltán Balázs, Lőrincz Dóra, Mayer Martin János, Molnár Alexandra, Neumer Tamás, Pálovics Péter, Patartics Bálint, Pázmán Koppány, Pető János, Szabó 928 Attila, Szélig Áron, Szigeti Bertalan György, Tamási Mátyás, Varju 105 Tamás, Vuchetich Bálint, Wirnhardt Bálint. 4 points: Kollarics Sándor, Miskó Gergely, Szilágyi 585 Dezső, Várnai Péter. 3 points: 10 students. 2 points: 8 students. 1 point: 20 students. Unfair, not evaluated: 1 solution.

Problems in Physics of KöMaL, April 2010