**P. 4694.** \(\displaystyle a)\) What is the amount of water in grams in the air of a room of volume 60 m\(\displaystyle {}^3\) at a temperature of \(\displaystyle 25~{}^\circ\)C, if the relative humidity is 50%?

\(\displaystyle b)\) To what per cent value does the relative humidity of the room increase if by the next morning the temperature of the room have decreased to \(\displaystyle 20~{}^\circ\)C? (The windows are closed and well sealed.)

\(\displaystyle c)\) What is the relative humidity of the same sample of air at a temperature of \(\displaystyle 10~{}^\circ\)C?

(4 points)

**P. 4698.** One end of a thread of length \(\displaystyle \ell\) is attached to a heavy iron ball, whilst the other end of the thread a feather is fixed, and the ball is projected in the horizontal direction. The ball flies through the metal ring shown in the *figure.* How long does it take for the thread to pass the metal ring?

*Data:* \(\displaystyle \ell=1.6\) m, \(\displaystyle h=1.25\) m, \(\displaystyle d=2\) m.

(5 points)

**P. 4699.** Two thin sheets on the surface of a slope of angle of elevation of \(\displaystyle \alpha=30^\circ\) form a pair of rails. The distance between the sheets is \(\displaystyle d=1.6\) cm. A ball of diameter of 2 cm is placed to the rails and it rolls down without slipping.

\(\displaystyle a)\) Calculate the acceleration of the centre of the ball.

\(\displaystyle b)\) If the coefficient of friction is \(\displaystyle \mu\), at what angle of elevation will the ball slip on the rails?

(5 points)

**P. 4701.** Small balls of charge \(\displaystyle Q\) are attached to the points \(\displaystyle P_1\) and \(\displaystyle P_2\) of a ring, made of some insulating material, moving in a vertical plane, such that \(\displaystyle \alpha=60^\circ\). The ring is in a homogeneous magnetic field of induction \(\displaystyle B\), the magnetic field lines are perpendicular to the plane of the ring. The ring is moved such that it rolls without skidding on the horizontal surface which is also made from some insulating material. The speed of the centre of the ring is \(\displaystyle v_0\).

\(\displaystyle a)\) What is the magnitude of the magnetic force exerted on each charge at the position shown in the *figure?*

\(\displaystyle b)\) At which positions of the ring will the torque of the sum of the magnetic forces calculated about the centre of the ring be zero? Considering only these positions, in which case will the force exerted by the magnetic field on the ring be the greatest and what is this greatest force?

\(\displaystyle c)\) Determine the intersection of the lines of action of the magnetic forces.

(5 points)

**P. 4702.** Four concrete cubes, which are made of different material, and which all have the side of 10 cm are placed next to each other as shown in the *figure.* They are ``illuminated'' by a beam of \(\displaystyle {}^{60}\)Co gamma-ray, from four different positions, (S1, S2, S3 and S4) one after the other. Opposite to the gamma source behind the cubes there are four detectors (D1, D2, D3 and D4). The first three measurements shows that the concrete cubes decrease the intensity of the radiation by 86.76, 71.94 and 84.25 percent of the original value, respectively.

\(\displaystyle a)\) What is the intensity of the radiation measured by the fourth detector, expressed in the percentage value of the intensity of the original radiation?

\(\displaystyle b)\) The ``thickness of the halving-layer'' of the first cube is 6 cm. What is this value for the other cubes (which is characteristic of the material of the cube)?

(5 points)