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Please read the rules of the competition.

Deadline expired on 11 January 2006.

M. 265. If the screen of a colour monitor or a colour television is observed through a magnifying lens then blue, green and red points or segments can be seen. Find the distance between two points or segments which have the same colour in both cases, with using optical devices.

(6 points)

Statistics

P. 3844. An electric kettle, rated at 6 W, is turned on for 25 minutes and 1.2 l water which was initially at a temperature of 20 ^{o}C is heated. Find the final temperature of the water if the efficiency of the process is 0.7.

(3 points)

P. 3845. In a football match can a goal be scored if the ball is kicked such that it undergoes only translational motion, hits the goal-post, then bounces on the goal-line, and then nobody touches the ball.

P. 3846. A hollow solid of revolution is rotated about its vertical axis of symmetry at an angular velocity of . What is the shape of this solid if a small object is in equilibrium at any point on the interior surface of the solid. (Static friction is negligible.)

(4 points)

P. 3847. To what potential should a spherical mercury drop be charged, if its electric potential energy is equal to its energy due to the surface tension. The diameter of the mercury drop is 2 mm.

P. 3848. A point-like light-source is placed to the symmetry axis of a hemisphere shaped piece of glass of radius 20 cm 10 cm away from the plane surface. The refractive index of glass is 1.5. How long does it take for the light ray whose angle of incidence is 60^{o} to travel through the glass, and what is its direction after emerging from the glass.

(5 points)

P. 3849. Electromagnetic plane wave is incident on and normal to a 10 m^{2} black plane surface, and it is totally absorbed by the surface. The greatest force exerted on the surface is 2^{.}10^{-18} N. Find the maximum of the electric field of the wave.

P. 3850. Radio waves are sent from the equator to a geostationary satellite, which can always be seen above our head. How long does it take the radio waves to reach the satellite, and what is the displacement of the satellite during this time?

P. 3851. A diffraction grating is illuminated by light of wavelength 598 nm. The distance between the lines in the diffraction pattern formed on a screen 5 m away from the grating is 2 cm. Find the distance between two rulings. How would the diffraction pattern change if half of the grating parallel to the rulings, or perpendicular to the rulings was covered?

P. 3852. With a special laser light impulses of an average wavelength of 600 nm are generated each of which lasts for 5^{.}10^{-15} seconds. Find the uncertainty of the wavelength of these photons.

P. 3853. Find the velocity of the object if its increase of mass is 10%.

a) By what percent will the length of the object decrease in the direction of the motion?

b) If its rest energy is W_{0}, what is its kinetic energy?