Mathematical and Physical Journal
for High Schools
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Problem P. 4227. (February 2010)

P. 4227. The density of an imaginary planet is 5.103 kg/m3, its radius is 5000 km. Inside the planet there is an enormous spherical hole, the radius of which is 1000 km, and whose centre is 3000 km from the geometric centre of the planet. What is the acceleration of that meteoroid which at one moment is at a distance of 6000 km from the geometric centre of the planet and the line segment which joins the centre of the planet and the meteoroid makes an angle of 60o with the line segment between the centres of the planet and the hole.

(5 pont)

Deadline expired on March 10, 2010.

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

Megoldás. $\displaystyle a=4{,}81~{\rm m/s}^2$.

Statistics:

 91 students sent a solution. 5 points: Alcer Dávid, Balogh Gábor, Barta Szilveszter Marcell, Batki Bálint, Burján Bence, Csopor Dávid, Czeller Ildikó, Dávid Bence, Ercsey Tamás, Farkas Martin, Filep Gábor, Fonai Dániel, Galgóczi Gábor, Galzó Ákos Ferenc, Hartstein Máté, Janosov Milán, Jéhn Zoltán, Kaposvári István, Kollarics Sándor, Kovács 255 Márton, Kovács 616 Philip, Kovács Attila, Kovács Márk, Kungl Ákos Ferenc, Laczkó Zoltán Balázs, Lájer Márton, Mayer Martin János, Molnár Alexandra, Nagy 111 Miklós, Nagy László Bendegúz, Pál Domonkos, Pálovics Péter, Pataki Bálint Ármin, Patartics Bálint, Pázmán Koppány, Pető János, Sándor Áron Endre, Sisák Mária Anna, Szélig Áron, Szikszai Lőrinc, Tamási Mátyás, Tóth 114 Viktor, Tóth 222 Barnabás, Varju 105 Tamás, Várnai Péter, Vuchetich Bálint, Wang Daqian. 4 points: 4 students. 3 points: 7 students. 2 points: 26 students. 1 point: 3 students. 0 point: 3 students. Unfair, not evaluated: 1 solution.

Problems in Physics of KöMaL, February 2010