Written exam in physics

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WRITING

EXAM
in physics is conducted in many universities across the country,
but only in three of them,
in addition to oral
There is also a written exam.
It’s done
at the Moscow Physico-Technical Institute,
as well as in physics departments
Moscow and Novosibirsk universities.
A written assignment usually contains 4-5 tasks.
It will respond to its execution
at the Physico-Technical Institute
5 o’clock
at Moscow State University and Novosibirsk State University - 4 hours.
Below are the options,
offered to applicants last year
to the Physico-Technical Institute and NSU.
Options
Faculty of Physics, Moscow State University
will be published
in the next issue of the magazine.

Option 1 (MIPT)

1. Two particles - one of mass $m$, flying with a speed of $v$, the other of mass $2m$, flying with a speed of $2v$, directed perpendicular to $v$ (Fig. 1) - are subject to forces of equal magnitude and direction for some time. By the time the forces cease, the right side turns and begins to move in the opposite direction at a speed of $2v$, as shown in figure. At what speed did the second part begin to move?

2. A vessel with a volume of 1.1 l contains 100 $e$ adsorbent and hydrogen at a temperature $t = -193^\circ$ C and a pressure $P = 0,2$ am. The adsorbent at this temperature absorbed hydrogen in an amount equal to $\frac{1}{50}$ the weight of the adsorbent itself. Determine the pressure in the vessel if it is heated to $t_1 = 31^\circ$ C, when all the hydrogen molecules leave the adsorbent. Adsorbent density $1 \frac{e}{cm^3}$.

3. Determine the resistivity of the metal if it is known that in each cubic

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4. An observer examines a distant object using an astronomical telescope (Kepler telescope). Lenses with focal lengths $F_1 = +30\text{ cm}$ and $F_2 = +5\text{ cm}$ are used as the object and eyepiece of the telescope. An observer sees a clear image of an object if the distance between the object and the eyepiece of the scope is between $L_1 = 33\text{ cm}$ and $L_2 = 34,5\text{ cm}$. At what distances are absences observed ranging from $L_1 = 33\text{ cm}$ to $L_2 = 34,5\text{ cm}$?

Option 2 (MIPT)

1. The flywheel of radius $R = 20\text{ cm}$ is mounted on a fixed axis of radius $r = 2\text{ cm}$. The friction force between the max wheel and the axle is constant and equal to 100 kg. To make it easier to remove the max wheel from the axis, a force $F = 8\text{ kГ}$ is applied to its rim, creating a torque relative to the axis (Fig. 2). With what minimum force $N$ do you need to pull the max wheel along the axis in order to remove it?

2. The pressure gauge consists of three glass tubes (Fig. 3). There is a pipe at the bottom of the pressure gauge, and oil in the left elbow above the pipe. How much does the pressure $P$, monitored by the pressure gauge, change if the oil level in the thin open tube rises by $\Delta h = 10\text{ mm}$? The ratio of the density of the pipe and oil is $\frac{\rho_1}{\rho_2} = 14$, and the ratio of the cross-sections of the tubes is $\frac{S_3}{S_2} = 2$, $\frac{S_2}{S_1} = 50$.

3. A flat capacitor with horizontal plates is connected to a battery with an emf. With. $U$ and placed in a vessel, which is gradually filled with kerosene ($\varepsilon = 2$). Write it down as a formula and graph the dependence of the field strength in the center of the capacitor on the thickness of the kerosene layer inside it. The distance between the plates of the capacitor is $d$.

4. The distance between an object and its direct and twice magnified image obtained using a thin lens is $L$. Find the optical power of the lens and find out the nature of the image (real or minimal).

Option 3 (NSU)

1. A square grid of uniform wiring consists of four identical square houses (Fig. 4). The resistance of one side of the cell is $r$. The current enters one corner of the grid and exits the opposite corner. Find the resistance of the entire grid.

2. Between the piston and the house of a cylindrical vessel filled with air, there is a partition with a hole closed with a stopper (Fig. 5). The pressure to the right of the septum is the same. When the piston moved, the plug flew out due to a pressure difference