Academic Year 2022 Actual

Physics entry test – session 1

1. A coal-fired plant generates 600 MW of electric power. The plant uses 4.8 × 106 kg of coal each day. The heat of combustion of coal is 3.3 × 107 J/kg. The steam that drives the turbines is at a temperature of 300◦ C, and the exhaust water is at 37◦ C. What is the overall efficiency of the plant for generating electric power?

(a) $33\%$;

(b) $39\%$;

(c) $46\%$;

(d) $54\%$.

2. Denoting T the temperature of a black body, and σ some constant, the Stefan-Boltzmann law that relates the radiant emittance M to T has the following form:

(a) $M = \sigma T$

(b) $M = \sigma T^2$

(c) $M = \sigma T^3$

(d) $M = \sigma T^4$

3. The food compartment of a refrigerator is maintained at $4^{\circ}C$ by removing heat from it at a rate of 360 kJ/min. If the required power input to the refrigerator is 2kW, what is the rate of heat rejection to the room where the refrigerator is?

(a) 250 kJ/min;

(b) 460 kJ/min;

(c) 870 kj/min;

(d) 480 kJ/min.

4. One considers 1 mol of carbon dioxide on the one hand, and $1mol$ 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 $H_2O$ molecules;

5. When from the Earth the phase of the Moon is seen as full, what phase of the Earth is then seen from the Moon?

(a) new;

(b) full;

(c) crescent;

(d) half;

6. The circuit shown in Fig. 6 is made of a dc generator delivering a fixed voltage, two switches, 1 and 2, five resistors with the same constant resistance $R$ and a light bulb with a fixed resistance. Because of the way the circuit is designed, the brightness of the bulb may vary as one closes the circuit using either or both of the switches. A particular sequence of on (circuit closd) and off (circuit open) states of the two switches will get the brightness of the light to increase from its minimum to its maximum. Choose the sequence that would do that:

sequence (a) both switches 1 and 2 on; switch 1 on only; switch 2 on only;

sequence (b) switch 2 on only; both switches 1 and 2 on;switch 1 on only;

sequence (c) whatever sequence is chosen, yields the same brightness as both the volt- age and the light bulb resistance are fixed;

sequence (d) switch 1 on only; switch 2 on only; both switches 1 and 2 on.

7. A battery is connected across two identical resistors in series. Assuming that one of the resistors is $\text{instantaneously}$ replaced by an uncharged capacitor, the current in the circuit:

(a) rises during particular while, and then falls;

(b) only rises;

(c) only falls;

(d) falls during particular while, and then rises;

8. 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;

9. Time-of-flight mass spectroscopy is a technique employed to determine p the mass of charged molecules. The basic equation used for that purpose reads: $\tau=\ell\sqrt{m/2q U}$, where $\tau$ is the time of flight, is the length of the analyzer tube, $m$ is the mass of the molecule, $q$ is its electric charge, and $U$ is the accelerating electric potential difference. In one experiment, the setup has the following characteristics: $\ell = 1.5 m$ and $U = 16 kV$. Assuming that the molecule has a charge $q = 1.6 \times 10^{−19} C$, and that the measured time of flight is $\tau = 30 μs$, the mass of the molecule is:

(a) $1.4 \times 10^{−12} kg$;

(b) $1.0 \times 10^{−24} kg$;

(c) $1.0 × 10^{−23} kg$;

(d) $2.0 × 10^{−24} kg$.

10. A ball is thrown straight upwards. As it reaches the top of its trajectory, its speed is zero, but what is the magnitude of its acceleration then?

(a) $0 m \cdot s^{−2}$ ;

(b) $4.905 m \cdot s^{−2}$ ;

(c) $9.81 m \cdot s^{−2}$ ;

(d) $19.62 m \cdot s^{−2}$;

11. 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) $\langle E_{\mathrm{{tot}}}\rangle = - 2 \langle V_{\mathrm{{tot}}}\rangle$;