**P. 4741.** A 20-litre gas cylinder just ``runs out'' of gas at the foot of a high hill next to the seashore. Then immediately the valve is closed, and the gas cylinder is carried up to the research laboratory at the top of the hill. Here some gas from the cylinder can again be used. When finally the gas cylinder is exhausted again its mass is measured, and it turns out that due to using the gas at the top of the hill its mass decreased by 4.1 grams. The air pressure at the top of the hill is 32 kPa less than at sea level. Both at the sea level and at the laboratory the temperature of the gas is \(\displaystyle 27~{}^\circ\)C, and the density of air at sea level is 1.2 kg/m\(\displaystyle {}^3\).

\(\displaystyle a)\) What type of gas was in the cylinder?

\(\displaystyle b)\) How high is the hill?

(4 points)

**P. 4743.** Two insulating threads, which have the same lengths, are suspended at the same point and at their lower end of each, there is a small ebony ball attached. The balls are given the same amount of like charges. The angle between the threads is \(\displaystyle 2\alpha=60^\circ\) when the pendulums are inside a container at rest in air. Then the container is filled with petroleum, such that both balls are in the petroleum, far from the walls of the container and from the surface of the liquid. What is the angle between the threads now?

*Data:* The density of ebony is \(\displaystyle 1200~{\rm
kg}/{\rm m^3}\), the density of petroleum is \(\displaystyle 820~{\rm kg}/{\rm m^3}\). The relative dielectric constant of petroleum is \(\displaystyle \varepsilon_{\rm r}=2\).

(5 points)

**P. 4746.** The following experiment is usually shown in order to demonstrate that light is a transverse wave:

A narrow parallel beam of natural light hits a plane glass, such that the reflected and the refracted rays are perpendicular to each other. Then another plane glass is used to reflect the reflected ray, such that the angle of incidence is the same as in the previous case. If this latter glass is rotated about an axis which coincides with the incident light ray, then it may happen that there is no reflected ray from this piece of glass.

\(\displaystyle a)\) How does this experiment proves that light is transverse wave?

\(\displaystyle b)\) What is the angle of incidence, if the refractive index of the glass is \(\displaystyle n=1.5\)?

\(\displaystyle c)\) What is the angle between the planes of the two pieces of glass when there is no reflected ray from the second glass?

(5 points)