Academic Year 2022 Sample

Physics entry test – session 1

1. Calculate the efficiency of a heat engine that during each cycle absorbs 64 kcal of heat and exhausts 42 kcal, operating during two cycles.

2. A radiant heating lamp has a temperature of 1000 K with emissivity factor e = 0.8. What should be the surface area to provide 250 W of radiation heat transfer?

3. 1 kg of ice at $0^{\circ}C$ and 1 kg of boiling water at $100^{\circ}C$ are mixed. What is the temperature of the mixture when all ice is liquefied?

4. The circuit shown in Fig. 4 is made of: a dc generator delivering a fixed voltage; four resistors such that $R_1$ and $R_3$ on the one hand are fixed and known, while on the other hand R is unknown and needs to be determined experimentally using $R_2$, which is adjustable; and a galvanometer. Find the condition using the fact that $R_2$ can be adjusted so that $R$ can be found; express $R$ as a function of the known parameters.

5. A $5m^3$ container is filled with 840 kg of granite (density is 2400 $kg \cdot m^3$) and the rest of the volume is air (density is 1.15 $kg \cdot m^3$). Find the mass of air present in the container.

6. Given that the power output of an engine is 50 kW and that its thermal efficiency is 24%, find the engine’s fuel consumption rate knowing that the fuel’s heating value is 44000 kJ/kg

7. Consider a car moving along a road at varying speed between two particular points A and B: the car accelerates and then decelerates. The mean speed measured between points A and B is 60 $km \cdot h^{−1}$. Is there at least one moment between the points A and B when the car reached exactly the speed of 60 $km \cdot h^{−1}$? Prove your answer mathematically.

8. A water filtration device can filter out a fraction $1 / n$ of impurity in the first pass of water through the device. At the next pass a fraction $1 / n$ of the amount removed during the previous stage. Find the value of $n_{\rm p}$ such that the water can be made pure. Knowing this value, explain what happens if $n = n_{\rm p}$

9. Two identical balls were charged in such a way that the charge of one of them turned out to be $n$ times greater in modulus than the other. The balls were brought into contact and then the distance between them was increased twice as far as before. How many times has the strength of their Coulomb interaction changed if their charges before contact were opposite?

10. What is the induction of the magnetic field in which a force of 50 mN acts on a conductor with an active part of 5 cm? The current in the conductor is 25 A. The conductor is located perpendicular to the magnetic induction.

11. Two bodies of equal mass are on a smooth horizontal surface and are connected by an inextensible rope of negligible mass. A force $F_1 = 7 N$ is applied to the first body, and a force $F_2 = 3 N$ to the second one. The forces are directed along one straight line in opposite directions. Determine the tension of the rope.

12. A homogeneous cylinder, with radius $R$, mass $m$ and moment of inertia $I$ around its axis, rolls without slipping on a horizontal tray. A translational motion is imposed on the tray, perpendicular to the axis of the cylinder, with a given time law $a(t)$. As a generalized coordinate, one can choose the angle $θ$ that specifies an arbitrary point of the cylinder along the horizontal direction. Show that the position $x$ of the center of the cylinder in the Galilean frame is linked to $θ$ by a holonomic constraint which is to be determined.