Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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Exercises and problems in Physics
December 2001

Please read The Conditions of the Problem Solving Competition.

Experimental problem

M. 229. On a smooth and dry horizontal plastic surface prepare a few water drops of different mass (e.g. with an eye-dropper). Examine the relation between the diameter and the mass of the water drops. (6 points)

Theoretical problems

P. 3478. Estimate how much work you do while you reach a proper press-up position from lying. (3 points)

P. 3479. Hydrogen gas is kept streaming through a tube while it is cooled by water surrounding the tube. The temperature of the incoming gas is 60 Co and that of the outgoing gas is 30 Co. The capacity of the cooler tank is 60 liter and the water in it is completely changed in every hour. The initial temperature of the cooling water is 10 Co and it is 20 Co when it is changed. What is the amount of the gas in kgs that goes through the tube in one hour? (4 points)

P. 3480. From a 5000 km radius planet a rocket is launched at the first cosmic velocity in a direction at a 60o angle to the vertical direction. What is the maximum height the rocket can reach? (5 points)

P. 3481. What is the relation between the temperature and the swing period of a physical pendulum made of a homogeneous material? (4 points)

P. 3482. On the middle one of three thin concentric spherical metal shells of radius R there is Q electric charge. The inner spherical shell of radius R_1={1\over2}R and the outer spherical shell of radius R_2={3\over2}R are earthed.

a) What is the amount of the electric charge on the earthed spherical shells?

b) Plot the electric field strength versus the distance from the centre. (5 points)

P. 3483. In the connection shown in the figure the switch K is open and the capacitor is uncharged. Then we close the switch and let the capacitor charge up to the maximum and open the switch again. Determine the values indicated by the ammeter

a) directly after closing the switch;

b) a long time after the switch was closed;

c) directly after reopening the switch;

U0=30 V, R1=10 kOmega, R2=5 k\(\displaystyle Omega\).) (4 points)

P. 3484. What should be the capacity of the adjustable capacitor shown in the figure so that the voltmeter indicates the highest voltage? (5 points)

P. 3485. The Sun attracts the Earth with a lot greater force then the Moon does.

a) What is the ratio of the two forces?

b) What is the explanation for the fact that despite this the tidal effect of the Moon is a few times bigger than that of the Sun. (5 points)

P. 3486. The binding energy of the 14N nucleus is 16.19 pJ and the 14C nucleus is 16.37 pJ. Which nucleus is the decay product of the other, and why? (5 points)

P. 3487. Werner Heisenberg, the Nobel Prize winner German theoretical physicist, was born a hundred years ago (5th December 1901). With the help of the uncertainty principle introduced by him estimate the uncertainty of the velocity of a carbon atom and an electron `sitting' on the point of a pine needle! (4 points)

Send your solutions to the following address:

    KöMaL Szerkesztőség (KöMaL feladatok),
    Budapest 112, Pf. 32. 1518, Hungary
or by e-mail to:

Deadline: 11 January 2002