# Exercises and problems in Physics

February 2003

## Please read The Conditions of the Problem Solving Competition.

## Experimental problem |

**M. 240.** Investigate the monochromaticity of different LEDs (light-emitting diodes) with optical grating. Determine in which interval is the wavelength of the emitted light.

(*6 points*)

## Theoretical problemsIt is allowed to send solutions for any number of problems, but final scores of students of grades 9-12 are computed from the 5 best score in each month. Final scores of students of grades 1-8 are computed from the 3 best scores in each month. |

**P. 3591.** Through the 3.5 m wide exit of an underground station 70 people are leaving each minute on average. The ``population density'' is 0.4 heads/m^{2}. How much is the average velocity of the people?

(*3 points*)

**P. 3592.** There is a circuit without any branches consisting of a galvanic cell, a battery and an ohmic resistance. The voltages that can be measured at the battery and at the resistance are both 9 V. What voltage can be measured at the galvanic cell (also 9 V) of non-zero internal resistance, and what can be said of the actual magnitude of the resistance?

(*4 points*)

**P. 3593.** A horizontal disc magnet of radius *R* rotates with an angular velocity of \(\displaystyle \omega\)_{0} around a fixed vertical axis going through its center. A similar horizontal disc, initially motionless, falls from a small distance on it and instantly sticks to it. (The centers of the two discs are closer to each other than *R*.) What is the common angular velocity the two discs rotate with?

(*4 points*)

**P. 3594.** A line pendulum is diverted perpendicularly, and released without pushing. Which section in the *figure* does the pendulum cover in a shorter time, *AP* or *PB*?

(*5 points*)

**P. 3595.** We prepare a hemisphere shaped depression inside a prism. The prism of mass *M* can freely move on the horizontal table. We release a point-like body of mass *m* at point *P* of the resting prism. What force does the prism exert on the small body in its state of angle \(\displaystyle \varphi\)? (Friction is negligible everywhere.)

(*5 points*)

**P. 3596.** There is oxygen gas in a 3 liter tank of a pressure of 2.2^{.}10^{6} Pa and a temperature of 80 ^{o}C, and in a 5 liter one of a pressure of 1.3^{.}10^{5} Pa and of a temperature of 5 ^{o}C. The two tanks are connected with a short pipe. What is the common pressure inside the tanks after they reach the room temperature, 23 ^{o}C? How much gas has flown through the pipe in the meantime?

(*4 points*)

**P. 3597.** A certain amount of noble gas picks up a *Q* amount of heat while its volume increases from *V*_{1} to *V*_{2}, and its pressure is proportionate to its volume. To what volume would the gas expand from the initial *V*_{1} volume if it absorbed heat *Q* while preserving its initial pressure? (*The data:* *V*_{1}=5 dm^{3}, *V*_{2}=8 dm^{3}.)

(*4 points*)

**P. 3598.** The plates of area *A* of a plane-parallel capacitor can slide along a horizontal insulator thread without friction. The mass of the left-side plate is *m* and its electric charge is *Q*, the mass of the right-side plate is 2*m* and its electric charge is -2*Q*. Initially the pates are fixed and their distance is 3*d*.

*a*) What is the energy of the electric field between the plates?

*b*) At a given moment they are unfixed. What is their velocity when their distance is reduced to *d*?

(*5 points*)

**P. 3599.** In Debrecen in 1984 it was determined that the activity concentration of the beta decay of the ^{85}Kr isotope, generated as a possible product of nuclear fission, is 0.8 Bq/m^{3}. Estimate how many krypton nuclei decay in one hour in the atmosphere.

(*5 points*)

**P. 3600.** Two grounded metal plates of large extents are including an \(\displaystyle \alpha\) angle with each other. In the bisector plane, in an *r* distance of the intersection line there is a thin stick of length *L* (*L*\(\displaystyle \gg\)*r*) which is charged uniformly with an overall electric charge of *Q*. What force is exerted on the stick due to the electrostatic induction, if *a*) \(\displaystyle \alpha\)=180^{o}, *b*) \(\displaystyle \alpha\)=18^{o}.

(*5 points*)

### Send your solutions to the following address:

- KöMaL Szerkesztőség (KöMaL feladatok),

Budapest 112, Pf. 32. 1518, Hungary