**M. 310.** Put a ping-pong ball onto the surface of the water in a glass, filled halfway. We experience that the ball moves next to the wall of the glass. Then fill the glass up to its rim, and place the ball again to the water. We can see that the ball moves to the centre of the glass. Examine experimentally, whether we experience the same or not if instead of the glass we use a wider vessel, for example a pot? What is the width of that vessel in which the experiment still ``works''? How does the time during which the ball moves to the wall, depends on the initial distance between the ball and the wall?

(6 points)

**P. 4298.** A carpet runner is placed onto a long straight inclined plane parallel to the steepest line in the plane, from the bottom of the slope till its top. The carpet is thin and flexible, and it cannot slide down because of the friction, but it can easily be lifted, it does not stick to the plane. The top end of the carpet is rolled, a bit, and this hoop of carpet is released. The hoop rolls down the slope with greater and greater speed, while its diameter increases, and finally it reaches the bottom of the slope during a time of *t*_{1}. If a solid cylinder is released at the top of the slope, it reaches the bottom in a time of *t*_{2}. *a*) Which motion lasts longer the motion of the carpet or the motion of the cylinder? *b*) Calculate the ratio of *t*_{1}/*t*_{2}.

(6 points)

**P. 4299.** A thin, solid uniform rod of length *L* is placed into a right-angled corner of a wall, and its point *A* at the bottom of the rod is moved at a uniform velocity of *v*_{A}, such that the rod always remains in the plane which is perpendicular to the wall and the floor. How far will the bottom end of the initially vertical rod be from the wall, when the top end is disconnected from the wall? (*Data: v*_{A}=3.5 m/s, *L*=2 m.)

(5 points)

**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**M*) is released at such a point, what is its relative speed at which it crosses the ring?

(5 points)

**P. 4302.** There is some Oxygen gas in a vertical, long enough, metal, cylinder, above a piston of mass *m*=60 kg, and of cross section *A*=2 dm^{2}. The cylinder is closed at its top and the piston hangs on a thread of length _{0}=11.2 dm. The initial pressure and temperature of the gas are equal to the pressure and temperature outside the cylinder, *p*_{0}=10^{5} Pa *T*_{0}=273 K, respectively. The wall of the cylinder is a good heat conductor, and the piston can move in the cylinder without friction. By what amount will the total energy of the system change if the thread breaks?

(4 points)