
Exercises and problems in Physics
October 2000 
New experimental problem:
M. 219. Balance straight rulers (laths) of different lengths on top
of a cylinder, in a position perpendicular to the axis of the
cylinder. Investigate how the period of the small oscillations of the rulers
depends on the length of the ruler. (6 points)
New problems:
P. 3374. A broad, high glass tube
stands on a table. A candle burns at the centre of the bottom of the tube and
there is a long, narrow glass tube above the candle as shown in the
figure.
P. 3375. A certain liquid in a capillary tube rises half as high as
water. What happens when some of this liquid is dripped next to one side of a
razor blade floating on top of water? (3 points)
P. 3376. One member of a group of tourists, Andrew, walks a little
faster than Brian, who started off earlier but walks more slowly. Andrew
observes when Brian passes a certain tree and measures (using his watch) that
he reaches the same tree time t_{1} later
than Brian, then catches up with Brian after another lapse of time
t_{2}. He says that he can work out the
proportion v_{A}/v_{B} of their respective speeds using these two time
data. How? (3 points)
P. 3377. A shot putter with a mass of 80 kg pushes the iron ball
with a mass of 6 kg from a standing position, at an angle of 45^{o} with the horizontal, accelerating it evenly during a
time interval of 0.1 seconds. The ball leaves his hand when it is 2 m high
above the ground and hits the ground 2 seconds later. What is the minimum value
of the static coefficient of friction if the shot putter does not slip during
the shot? (5 points)
P. 3378. The plates of a charged plane capacitor are at 3 cm
from each other. A 3 mm thick, uncharged metal plate is pushed between
them. Do the pd. and energy of the capacitor change? Is any work done while
pushing the plate into position? (4 points)
P. 3379. Consumers with respective resistances of 100 , 200 , 300 and
400 are connected in such a way that
they take up a total power of 100 W when connected to a pd. of
100 V. What power does each consumer take up in this situation? (4 points)
P. 3380. A light source that can be considered as pointlike is
placed next to a 8.4 mm thick glass panel. Looking at the glass from the
side of the light source, at almost rightangles to the glass, several images
can be seen at distances of 12 mm from each other. Determine the
refractive index of the glass. (5 points)
P. 3381. A straight conductor of length
l moves at velocity v in a homogeneous magnetic field of
induction B. What is the pd. between the ends of the conductor if the
angle between the wire and the magnetic induction is , that between the induction and the velocity is and that between the velocity and the conductor
is ? (E.g. let =30^{o}, =40^{o}, =50^{o}, l=0.5 m,
v=2 m/s and B=0.5 mT.) (5 points)
P. 3382. Leó Szilárd and Walter Zinn measured that the average number
of neutrons produced in the course of the fission of ^{235}U is 2.5. Consider 100 nuclear fissions in an imaginary
reactor. Among the neutrons produced in these fissions, 10 escape from the
reactor, 8 are captured in ^{238}U, some are
absorbed by the control rods and the rest induce further fissions. How many
percents of the neutrons have to be absorbed by the control rods in order to
sustain a constant number of neutrons in time? (3 points)
P. 3383. Half of the inner surface of a glass tube is covered with
soot, the other half with some reflecting material. The tube is placed
vertically onto the table with its black half downward as shown in figure
(a). There is a pointlike photodetector D on the table, on the axis of
the tube. How many times is the value read by the photodetector higher when
the tube is turned as shown in figure (b)? (5 points)
Send your solutions to the following address:
KöMaL Szerkesztőség (KöMaL feladatok),
Budapest Pf. 47. 1255, Hungary
or by email to: solutions@komal.elte.hu.
Deadline: 13 November 2000
