**P. 4278.** A U-shaped communicating vessel, made of a bent glass tube, contains water. The part of the tube which is filled with water is 30 cm long. The difference between the levels of the water in the two parts of the tube is 1 cm when the communicating vessel is in a vehicle which accelerates uniformly.

What is the acceleration of the vehicle if the length of the part of the tube which is horizontal is 10 cm? What would have the difference between the lengths of the water columns been, if a V-shaped communicating vessel had been used in which the total length of the tube which is filled with water was also 30 cm?

(5 points)

**P. 4279.** A rubber ball is dropped in a lift, which is at rest, from a height of 2 meters, and first it bounces back to a height of 162 cm. How much time elapses between the first and the second bounces? Then the experiment is repeated, such that the lift accelerates upward with a constant acceleration of 1 m/s^{2}. Will the rebouncing heights and the time between two consecutive bounces change? If yes, how?

(5 points)

**P. 4281.** Using six *different* resistors the tetrahedron *ABCD* was soldered. If a battery is inserted between two vertices (for example *A*, *B*) and a sensitive ammeter is inserted between other two vertices (*C*, *D*), then we experience with a surprise that the ammeter reads zero, independently of the two vertices of the tetrahedron which were chosen first.

What is the relation between the six resistances?

(4 points)