## Exercises and problems in Physics |

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

## New experimental problem:

**M. 210. **A test tube with some ballast at its bottom (water, shots,
sand, etc.) floats in water in a vertical position, in a large
graduated cylinder. When the test tube is slightly lifted and
released, it makes vertical damped oscillations. Measure the period
*T *of the oscillations (with different quantities of ballast)
and calculate the value of the quantity . Compare *x *with the length of the test tube
immersed in water when the tube is at rest. (6 points)

## New problems:

**P. 3284. **A closed ring made
of some metal wire has a piece of wire soldered to each end of a
quarter cycle of the ring as shown in the *figure*. Connecting
these pieces of wire to a current supply, a current of 2.4 A
starts flowing. What are the separate resistances of the quarter and
the three-quarter cycles, if a pd. of 3.6 V is measured between
the soldering points? What is the power taken up by the metal ring? (3 points)

**P. 3285. **A balloon with a mass of 7.3 kg, filled with
helium gas at a temperature of 23^{o} C, floats in the air as a sphere with a
diameter of 2.4 m (it does neither rise, nor sink). The density of air
around it is 1.19 km/m^{3}.

What is the pressure of the helium gas? (4 points)

**P. 3286. **Silvia asks her
friend Julia for help through the Internet, to solve the following
physics problem:

*"The figure represents some equilibrium process of n moles of
monatomic ideal gas. How much heat does the gas take up during the
process?"
*

Unfortunately, it turned out later that Silvia had typed wrong
data on the vertical axis. The correct figure has symbols
*p* instead of *T*.

How many times is the correct result greater than what Julia first
calculated, assuming that the initial temperature of the gas is
*T*_{0} in the correct figure as
well? (4 points)

**P. 3287. **A stone is thrown horizontally with initial
velocity *v*_{0}. What is the time
dependence of the angular velocity of this velocity vector? (5 points)

**P. 3288. **What is the maximum starting acceleration - on
level ground - of a motorcycle with a very strong engine if the wheel
base is *l*, the height of the centre of gravity is *h *and
the coefficient of friction between the wheels and the ground is ? The moment of inertia of the wheels is
small, the load on the wheels is identical in equilibrium. (5 points)

**P. 3289. **There are two electric dipoles in vacuum, at a
distance of 3 m from each other, with respective electric dipole
moments of 6^{.}10^{-6} C m and 2^{.}10^{-7} C m. (The dipoles can be
approximated as pairs of charges.) What are the minimum and maximum
values of the interaction energy between the two dipoles? (The
point-like charges forming the dipoles are in both cases in one
straight line.) (6 points)

**P. 3290. **A proton beam passes first through a 4 cm
wide, homogeneous magnetic field with induction *B*_{1}=0.2 T, and then through a second, also
4 cm wide, homogeneous magnetic field joining the first field,
but with induction *B*_{2}=0.4 T. The *B*-lines of the two
fields are parallel and point into the same direction; the initial
velocity of the protons is perpendicular both to the *B*-lines
and to the limiting surface of the magnetic fields.

What accelerating voltage is required so that the protons can penetrate through both magnetic fields? (4 points)

**P. 3291. **What is the difference in percentage between the
wavelength of the smallest frequency visible light emitted by
deuterium and hydrogen atoms? (5 points)

**P. 3292. **Sometimes, interesting colourful streaks can be
observed on a transparent plastic ruler lying on a table by the
window. Give an explanation to the phenomenon. (5 points)

**P. 3293. **There is a body of mass *m *at the bottom of a
thin and narrow tyre of mass *m *and radius *r *standing on
a level table. The small body is started with a small, horizontal
initial velocity *v*_{0} in the
plane of the tyre. How does the centre of the tyre move afterwards?
(Friction is negligible everywhere.) (6 points)