Academic Year 2023

Physics entry test – session 3

1. One considers 1 mol of carbon dioxide on the one hand, and 1 mol of water on the other hand. Knowing that the molar mass of carbon dioxide is larger than that of the water vapor, the exact number of $CO_2$ molecules is

(a) larger than the number of $H_2O$ molecules;

(b) the same the number of $H_2O$ molecules

(c) smaller than the number of $H_2O$ moleculesi

(d) one cannot compare these two numbers as the molecules are different

2. The motor of a cordless screwdriver powered by a battery consumes 295 W of electrical power and delivers a useful mechanical power of 210 W. Knowing that the insertion of a screw into a wall plug necessitates 4 seconds, what is the efficiency of the electrical motor?

(a) 4 s as the efficiency is evaluated considering the time needed for the operation

(b) $60\%$

(c) $28\%$

(d) there is no such a thing as an electrical motor efficiency

3. A coal-fired plant generates 600 MW of electric power. The plant uses $4.8 × 10^6 kg$ of coal each day. The heat of combustion of coal is $3.3 ×10^7 J/kg$. The steam that drives the turbines is at a temperature of $300^{◦}\text{C}$, and the exhaust water is at $37^{◦}\text{C}$. What is the overall efficiency of the plant for generating electric power?

(a) $33\%$ (b) $39\%$ (c) $46\%$ (d) $54\%$

4. In a power plant, water drives a turbine used for the generation of electrical power. The speed of water throughout the circuit that leads to the turbine is $17 m·s^{−1}$, and the volumetric flow is $5 m^3 ·s^{−1}.$ The turbine delivers a mechanical power of 300 kW to the electrical generator. The turbine’s efficiency is:

(a) $89\%$ (b) $72\%$ (c) $36\%$ (d) $41\%$

5. When an object with surface area A moves at high speed $v$ in a fluid, a drag force $F$ is exerted on it. A formula for $F$ is $F = Aγv2$, where $γ$ is a quantity that has the dimension of:

(a) an acceleration;

(b) a length;

(c) a density;

(d) a mass;

6. A probe sent to a distant planet lands on top of a cliff, 100 m above sea level. Its optical system scans the environment and data shows that the horizon in all directions appears to be at an angle of 5 mrad below the local horizontal plane. This information suffices to estimate the radius of the planet at sea level. How far is the horizon line from the probe?

(a) 15 km;

(b) 27 km;

(c) 40 km;

(d) 52 km.

7. The virial theorem establishes a particular relationship between the time averaged total kinetic energy $\langle K_{\mathrm{{tot}}}\rangle$of an assembly of particles and the time averaged total interaction potential energy $\langle V_{\mathrm{{tot}}}\rangle$in the system due to the two-body interaction between any two particles. If the interaction potential has the form: $V = ar^n$, with $r$ being the interparticle distance, and a is some constant, then the virial theorem takes the form: $\langle K_{\mathrm{{tot}}} \rangle\;=\;\frac{n}{2} \langle V_{\mathrm{{tot}}} \rangle$. Now, assume that $V = ar$; then what is the time averaged total energy $\langle E_{\mathrm{{tot}}}\rangle$?

a) $\langle E_{\mathrm{{tot}}}\rangle = 0$;

(b) $\langle E_{\mathrm{{tot}}}\rangle = \langle V_{\mathrm{{tot}}}\rangle / 2$;

(c) $\langle E_{\mathrm{{tot}}}\rangle = 2 \langle V_{\mathrm{{tot}}}\rangle$;

(d) $\langle E_{\mathrm{{tot}}}\rangle = - 2 \langle V_{\mathrm{{tot}}}\rangle$;

8. A 10 mT magnetic field acts on a conductor, in which the electrical current intensity is 50 A. Assuming that the field induction lines and the direction of the electrical current are perpendicular, and that the length of the active part of the conductor is 0.1 m, what is the magnitude of the force acting on it?

(a) 0.5 N;

(b) 0.025 N;

(c) 0.25 N;

(d) 0.05 N.

9. How will the force of the Coulomb interaction between two small charged balls change when the electric charge of each of these decreases by a factor of 2, assuming that the distance between the balls remains unchanged?

(a) it will not change;

(b) it will decrease by 2 times ;

(c) it will decrease by 4 times;

(d) it will increase by 2 times.

10. Four electrical charges $Q$ are located at the corner of a square whose sides are equal to a. Since all charges are equal in magnitude, the magnitude $F$ of the electrostatic force $F$ acting on each charge is the same for all charges. Letting the constant $k=1/\left(4\pi\varepsilon_{0}\right)$, the calculation of $F$ yields the following expression:

(a) $F = 0$ as because of symmetry reasons, the forces cancel out

(b) $F=\frac{(1+2\sqrt{2})k Q^{2}}{2a^{2}};$

(c) $F=\frac{k Q^{2}}{2a^{2}};$

(d) $F=\frac{4 k Q^{2}}{2a^{2}};$