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Problem P. 4301. (December 2010)

P. 4301. The radius of a thin ring of mass M floating in space is R.

a) At which point of the straight line which goes through the centre of the ring and which is perpendicular to the plane of the ring will the force exerted on a small pointlike object be the greatest? (Where will the gravitational field strength be the greatest?)

b) If a pointlike object of mass m (m\llM) is released at such a point, what is its relative speed at which it crosses the ring?

(5 pont)

Deadline expired on January 10, 2011.


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

Megoldás. \(\displaystyle a)\) A gyűrű tengelyén a középponttól \(\displaystyle R/\sqrt{2}\) távolságra lesz maximális a gravitációs térerősség.

\(\displaystyle b)\) A kis test \(\displaystyle \sqrt{\left(2-\sqrt{\frac{8}{3}}\right)\gamma\frac{M}{R}}\approx 0,\!606\sqrt{\gamma\frac{M}{R}}\) relatív sebességgel halad át a gyűrű középpontján.


Statistics:

65 students sent a solution.
5 points:Antalicz Balázs, Ayhan Dániel, Gargauly Gergő János, Horicsányi Attila, Jéhn Zoltán, Juhász Péter, Kovács 444 Áron, Laczkó Zoltán Balázs, Mázik László, Nagy 111 Miklós, Nagy Lajos, Park Choong Eun, Pataki Bálint Ármin, Pázmán Koppány, Pázmán Zalán, Pető János, Tossenberger Tamás, Ürge László, Vuchetich Bálint.
4 points:Bajnok Eszter, Batki Bálint, Bolgár Dániel, Fülep Andrea , Gál Szabolcs, Szabó 928 Attila, Szemes Gábor Bence, Szikszai Lőrinc, Varga 515 Balázs, Vécsey Máté.
3 points:18 students.
2 points:5 students.
1 point:8 students.
0 point:3 students.
Unfair, not evaluated:2 solutions.

Problems in Physics of KöMaL, December 2010