Written exam in physics at the physics department of Moscow State University

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UPON ADMISSION TO THE PHYSICS FACULTY OF MSU
applicants will take two exams in physics:
written and oral.
In 1969, the written exam offered a test consisting of five problems. It took four hours to solve it.
Two versions of the 1969 test are published here. On page 61 the answers to the tasks are given and the obligations for solving some of them are given.

Option 1

1. A hockey puck, on the ice, passes successively two equal segments of a path of length $l$ each and continues to move. She completes the first segment in $t$ seconds, the second in $2t$ seconds. Find the speed of the puck at the end of the first segment of the path if the resistance to movement is assumed to be constant.

2. In the heat-conducting state, we find arcs of liquid with specific thermal capacities $c_1$ and $c_2$, separated by a non-teleconducting partition. The temperature of one fluid is greater than the other. The partition is removed, and after thermal equilibrium is established, the difference between the initial temperature of one of the liquids and the temperature established in the saucepan turns out to be half the difference in the initial temperatures of the liquid. Find the ratio of masses $m_1$ and $m_2$ of the first and second liquid.

3. In the circuit shown in figure 1, initially all the switches are open and the capacitors are discharged. Then the keys $K_1$ and $K_2$ are closed, and the key $K_3$ remains open. After some time, keys $K_1$ and $K_2$ are opened, and key $K_3$ is closed. Find the charge on capacitor $C_1$ after the indicated switchings. The capacitance of the capacitor and the emf of the batteries are indicated in figure letters.

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4. Two flat mirrors $3_1$ and $3_2$ (Fig. 2) are installed close to each other at an angle $a=15^\circ$ to the vertical. A thin converging lens is placed at a distance of $L=8,3$ cm from the mirror connection line so that its main optical axis is perpedicular to the mirror connection line. Between the mirrors and the lens on the main optical axis of the lens at a distance of $R=2$ cm from the mirror connection line there is a point light source $H$. Determine the distance between the images of the light source that are obtained using the lens. The focal length of the lens is $f=8$ cm. The partition $K$ protects the lens from rays and light from the light source.

5. A ball $A$ of mass $m$, fixed on a long weightless spoke, forms a pendulum, which can oscillate, curing around the axis $O$ (Fig. 3). The ball $A$ is deflected to a height $h$ and released without initial velocity. At the bottom point of its trajectory, the ball $A$ is contained with two balls $B$ moving towards it, the mass of which is $M$. The ball $B$, like the ball $A$, is fixed on a long weightless knitting needle, moving around the axis $O_1$. Immediately before the collision, the velocities of the balls are directed along the lines connecting their centers. What speed $v$ must the ball $^1$ $B$ have before the collision so that the ball $A$ rises to the same height $h$ after the collision? The impact is absolutely elastic. Friction in wasps and ovozdux should not be taken into account.

Option 2

1. A small lead ball of volume $V=0,02$ $cm^3$ falls uniformly in water. How much heat will be released when the ball moves down 6 m? The density of lead is $\rho=11,3$ $e/cm^3$. Accept $g=10$ $m/cek^2$.

2. A thin converging lens with a focal length $f=10$ $cm$ is cut in half along the diameter and its halves $J-L$ (Fig. 4) are mixed relative to each other along the main optical axis at a distance $l=10$ $cm$. At a distance $a=30$ $cm$ from the upper half of the lens, a mirror is installed on the main optical axis, shown in figure 5. With what acceleration will the cart begin to move along the floor if a force $F=8$ $cm$, directed vertically upward, is applied to the free end of the rope. Friction coefficient between load and trolley $k=0,6$. Accept $g=10$ $m/cek^2$.

3. A low trolley weighing $P=12,5$ $k\Gamma$ can move on a horizontal floor without friction. There is a load on the cart weighing $P_1=10$ $k\Gamma$. A rope is attached to the load, throwing a weightless block mounted on the cart, as shown in figure 5. With what acceleration will the cart begin to move along the floor if a force $F=8$ $cm$, directed vertically upward, is applied to the free end of the rope. Friction coefficient between load and trolley $k=0,6$. Accept $g=10$ $m/cek^2$.