**P. 4685.** The object of mass \(\displaystyle M=4m\), shown in the *figure* can freely slide along the horizontal. The curved part of its surface is horizontal at its right side. A small body of mass \(\displaystyle m\) is placed to the object of mass \(\displaystyle M\) at a height of \(\displaystyle H\), measured from the horizontal tabletop, and then the system is released. When the small object of mass \(\displaystyle m\) hits the table the two objects are at a distance of \(\displaystyle d=0.6\) m. Friction is negligible everywhere and \(\displaystyle h=0.2\) m.

\(\displaystyle a)\) What are the speeds of the two objects at the moment when the small one of mass \(\displaystyle m\) leaves the big one of mass \(\displaystyle M\)?

\(\displaystyle b)\) At what speed does the small object hit the table?

\(\displaystyle c)\) Calculate the height \(\displaystyle H\).

(4 points)

**Deadline expired on 12 January 2015.**