**P. 4329.** The jib of a tower crane is *L*=40 m long and it rotates about one of its ends in a horizontal plane at a constant angular speed of =0.03 s^{-1}. On the jib a trolley moves away from the fixed end of the jib at a speed of *u*=0.08 m/s, with respect to the jib.

*a*) Determine the speed of the trolley with respect to the ground as a function of time.

*b*) Graph the path of the trolley with respect to the ground as it moves along the jib.

*c*) Determine the velocity of the trolley with respect to the ground as a function of time.

(4 points)

**P. 4331.** One third of the space in a hollow sphere of inner diameter 8 cm is filled with water. The sphere is floating freely in a space station. What is the position of the water if the material of the sphere is

*a*) glass, to which water totally adheres,

*b*) silver, and the contact angle between the silver and the water is 90^{o}?

(5 points)

**P. 4334.** In a container which is equipped with a piston there is a mixture of Oxygen and Nitrogen gas at a temperature of *T*=77.4 K. Keeping the temperature constant the mixture is slowly compressed. The pressure of the mixture as a function of the volume changes as shown in the *figure,* where *V*_{1}=15 dm^{3} és *p*_{1}=56.3 kPa.

*a*) How much Oxygen and Nitrogen are there in the container?

*b*) Determine the coordinates of that single point on the isotherm, where the graph has a cusp.

(5 points)

**P. 4335.** The electromotive force of the voltage supply in the circuit, shown in the *figure,* is *U*_{0}=9 V and its internal resistance *R*_{b} is unknown. The resistances of the meters and the resistor are also unknown. When the switch is closed then the measured current increases to twice of the previous value, and the reading on the voltmeter decreases to half of the original value.

*a*) By what factor is the resistance of the voltmeter greater than that of the resistor?

*b*) What are the readings on the voltmeter before and after closing the switch?

(4 points)