## Exercises and problems in Physics |

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

## New experimental problem:

**M. 216. **"Why does a magnetic steel rod have no
effect at its middle, but a stronger and stronger effect towards its
ends?" - asked Ányos Jedlik (1800 - 1895) famous Hungarian
professor of Physics in the course of an examination, in 1871. Measure
the direction of the magnetic induction *B *around a rod magnet
and represent the field using *B*-lines.

## New problems:

**P. 3344. **The horizontal rotating disc of a bicycle
dynamo touches the wheel of radius *R *exactly above the axle of
the wheel, at distance *r *from the axle. The disc and the wheel
roll without sliding on each other, and the wheel rolls similarly on
the ground. At what speed does the point of the disc opposite to the
touching point travel forward when the bicycle travels at speed
*v*?

**P. 3345. **A solid cylinder of mass
*m*=6 kg and radius *r*=0.1 m is kept in balance
on a slope of inclination =30^{o} with the help
of a thread fastened to its jacket. The cylinder does not slip on the
slope.

*a*) What force *F *is
required to keep the cylinder in balance when the thread is held
vertically?

*b*) In what direction should the thread be pulled to minimise
the force required to hold the cylinder? What is the magnitude of this
force?

*c*) What is the minimum required coefficient of friction in
cases *a*) and *b*)?

**P. 3346. **A
well-fitting disc of negligible mass is pressed against the bottom of
a cone-frustum jacket type vessel broader at the bottom. The vessel is
then immersed into the water container shown in the figure and
fastened to the container by its jacket. The volume of the displaced
water is 1 dm^{3}. A piece of ice
with a mass slightly greater than 1 kg is then placed onto the
disc. What happens when the ice melts?

**P. 3347. **How many times should the mass of the
point-like body hanging on a thread be greater than that of the thread
so that the period of such a pendulum differs by no more than 1 % from
that of a mathematical pendulum?

**P. 3348. **The long, horizontal pair of rails shown
in the figure is connected using resistance *R*. The distance
between the rails is *l*, the electrical resistance of the rails
is negligible. A conducting rod of mass *m *and length *l
*can slide without friction on the pair of rails, in a vertical,
homogeneous magnetic field of induction **B**.

A force of magnitude *F*_{0} is
exerted for a long time onto the conducting rod, therefore the speed
of the rod is constant. The external force stops at a certain point
*P*. What distance does the conducting rod cover from point *P
*before stopping?

**P. 3349. **There are two identical superconducting
rings at a large distance from each other. Current *I*_{0} flows in one of them (*A*), and no current
flows in the other one (*B*). The two rings are slowly approached
to each other. What is the current flowing in *A *when current
*I*_{1} flows in the other ring?
(The value of the magnetic flux surrounded by a superconducting ring
cannot change.)

**P. 3350. **A small
body of mass *m *is at rest inside a thin, narrow tyre of mass
*M *and radius *r *lying on a horizontal table, touching the
tyre. How does the centre of the tyre move if the small body starts to
move at a tangential initial velocity *v*_{0}? How much later and where will the velocity of
the tyre be zero again? (Friction is everywhere negligible.)

**P. 3351. **A point-like body of mass *m *moving
without friction at speed *v*_{0}
collides elastically with a system *S *consisting of two
point-like bodies of mass *M *each, joined to each other by a
spring of directional force *k*.

*a*) What should the minimum value of the proportion
*m*/*M *be so that a second collision occurs between the
body of mass *m *and the system *S*?

*b*) What is the maximum time elapsing between the two
collisions?