**P. 3886.** In the end of 2005 when the row broke out over the price of natural gas between Ukraine and Russia, Hungary had a storage of 2.4^{.}10^{9} m^{3} (standard form) natural gas. In Hungary to store the gas, exhausted gas or oil fields are used which are filled with water (e.g. near Hajdúszoboszló) and the gas is compressed into these reservoirs under a pressure of 200 bar.

*a*) At what maximum depth can these reservoirs be?

*b*) In Hungary what is the least useful volume of these reservoirs?

*c*) The stored gas is mainly methane. Estimate the total mass of the compressed gas.

*d*) Natural gas is cooled down under the temperature of -160 ^{o}C, and condensed. The density of the gas increases to 600 times of the density when the gas is at standard temperature and pressure. How many oil-tankers can be filled with the gas described above if the volume of one tanker is 160 000 cubic metre?

(4 points)

**P. 3888.** A man is walking along a straight road from point *A* to point *B* with a uniform speed. Point *O* is on the perpendicular bisector of the line segment *AB*, and at *O* there is a man who is beating a drum. Another day another man is walking from *A* to *B*, with the same speed as the first man was walking, and plays the drum, while an observer listens at point *O*. In which case does the observer count more beats while the man moves from *A* to *B*? (The beating starts in both cases well before the man leaves *A*, and lasts at least until the man reaches *B*. The beating is uniform, its period is the same in both cases and much smaller than the time needed to walk from *A* to *B*.)

(5 points)

**P. 3889.** A syringe is filled with water. Its volume is 20 cm^{3}, and the cross section of its interior part is 4 cm^{2}. The syringe is held vertically such that its nozzle is at its top, and its 100 g piston is pressed and moves with a constant speed. The ejected water has an initial upward velocity of 2 m/s, and the cross-section of the beam of water at the nozzle is 1 mm^{2}. (Neglect the dissipated energy due to friction.)

*a*) Find the speed of the piston.

*b*) What is the total work done by us?

*c*) Express and graph the force exerted on the piston as a function of time.

(4 points)

**P. 3890.** A charged metal sheet is placed into uniform electric field, perpendicularly to the electric field lines. After placing the sheet into the field, the electric field on the left side of the sheet will be *E*_{1}=5.6^{.}10^{5} V/m and on the right it will be *E*_{2}=3.1^{.}10^{5} V/m (see the *figure*).

*a*) Find the total charge of the sheet if you know that a force of 0.08 N is exerted on it.

*b*) Find the area of the sheet.

(5 points)