**P. 4605.** The terminal voltages of the power supplies shown in the *figure* are constant, and the values of the terminal voltage are: *U*_{1}=15 V and *U*_{2}=45 V. The resistances of the resistors are *R*_{1}=10 and *R*_{2}=20 .

*a*) What are the readings shown by the meters, which are considered ideal?

*b*) Solve the problem, if the two meters are swapped over.

(3 points)

**P. 4609.** Both ends of a horizontal thin tube are closed. There is a mercury thread of length *h* at the middle of the tube. The length of the air columns in both parts is , and the pressure of both air columns is equal to the gauge pressure of a mercury column of height *H*. The tube is placed to a tumble dryer, the symmetry axis of which is vertical, and the tumble drier is started to spin.

Give the displacement of the mercury thread as a function of the angular speed , if the temperature is constant.

(5 points)

**P. 4610.** There is a sample of ideal gas in a cylinder shaped container. The symmetry axis of the cylinder is horizontal and at one end it is closed by frictionlessly moveable piston. Initially the volume of the gas is *V*_{1}, its temperature is *T*_{1} and its pressure is *p*_{1}, which is the same as the ambient (and later on as well constant) air pressure.

The sample of gas is taken through the following processes *n* times: It is heated at constant pressure to a temperature of *T*_{2}, and then it is cooled back to the temperature of *T*_{1} keeping its volume constant at its reached value. While the gas is heated at constant pressure an external constant force is exerted on the piston, which force is different at the different heating steps. During the whole process the total work done is *W*.

*a*) To what value will the volume of the gas increase after the *n*-th step?

*b*) What is the total work *W* done by the external force?

(5 points)

**P. 4612.** An object, which is at a distance of 30 cm from us, is observed through a lens. When the lens is close either to us or to the object then the object seems to have its original size, but when the lens is in between these two positions the object appears bigger.

*a*) Where is the lens when the object appears the greatest?

*b*) What is the focal length of the lens, if when the object appears the greatest, its observed size is twice as big as its original size?

(5 points)

**P. 4613.** A uniform, 1-metre long uninsulated resistance wire, the cross section of which is everywhere constant, is connected to a power supply, the terminal voltage of which is stabilized. One terminal of a resistor, whose resistance is the same as the resistance wire is connected to the end of the resistance wire, whilst the other terminal is moved along the resistance wire.

Where is the pointer of the moving terminal, when the power dissipated on the resistor is one-quarterth of the maximum power dissipated at the resistor?

(4 points)

**P. 4614.** The linear charge density of a very long, straight, vertical insulating thread is =8^{.}10^{-7} C/m. A very small metal ball of charge *q*=6.81^{.}10^{-8} C is suspended by a very thin insulating thread of length =10 cm, which is at a distance of *d*_{0}=5 cm from the other thread. The metal ball is fixed with an insulating equipment at the position in which the thread is vertical. At a given moment the ball is released from its fixed position without any push. Determine

*a*) the maximum distance between the vertical metal thread and the ball;

*b*) the angle between the vertical and the supporting thread of the ball, when the speed of the ball is maximum.

(5 points)

**P. 4615.** A slinky, a helical spring (used as a toy which is able to travel down a flight of steps) whose unstretched length is negligibly small, obeys Hooke's law with a good approximation, and it has a considerable elongation due to its own weight.

*a*) The slinky of mass *m* resting on the table is slowly raised at its top end until its lower end just raised from the table. The length of the spring at this position is *L*. How much work was done during lifting the spring?

*b*) If the slinky is released from this position, interestingly its lowermost turn does not move until the whole spring reaches its totally compressed length, (see the *figure*). What is the initial speed of the slinky at which it begins to fall right after reaching its totally compressed position?

(6 points)