**P. 4551.** There is a massless piston, which can move frictionlessly, in the middle of a 1-metre long, horizontal tube, closed at both of its ends. In the left chamber there is a sample of Oxygen gas, and in the right chamber there is Hydrogen gas at the same tempereture. The mass of the hydrogen is one-fourth of that of the Oxygen. Where is the equilibrium position of the piston?

(3 points)

**P. 4557.** A 0.6-kg iron cylinder is attached to the end of the spring shown in the *figure,* and a disc shape magnet of mass 0.2 kg sticks to the bottom of the iron cylinder. Initially the spring, the spring constant of which is 64 N/m, is unstretched, and then the system is released. During the oscillation the magnet does not fall off.

*a*) What is the period of the oscillation?

*b*) What is the greatest speed of the magnet?

*c*) What is the minimum force between the magnet and the iron cylinder?

(4 points)

**P. 4558.** There is some water and its saturated vapour above it in a container, containing a piston, at a temperature of 370 ^{o}C. The total mass of the water and its vapour is 2 kg. The initial volume of the water and its vapour together is 8 dm^{3}.

*a*) What is the volume of the vapour?

*b*) The piston is moved into the vessel, while the temperature is kept constant, and the volume of the container is decreased to 5 dm^{3}. What will the volume of the water vapour be in this case?

*c*) By how many molecules did the amount of vapour decrease?

(4 points)

**P. 4559.** A pen dosimeter, which contains 5 cm^{3} air at standard conditions, and which has a capacitance of 1 pF, is charged to 1000 V, initially. What is the absorbed doze, if after the exposure, the voltage drops to 900 V? The average ionization-energy of air is 6.88 aJ and its density is 1.3 kg/m^{3}.

(4 points)