MikaStars39/nano-eval huggingface dataset:
Suppose the expression for the open-loop frequency response of a certain integrated operational amplifier is
$$
\dot{A}_{*}=\frac{10^{3}}{\left( 1+\mathrm{j} \, \frac{f}{f_{\mathrm{H1}}} \right) \left( 1+\mathrm{j} \, \frac{f}{f_{\mathrm{H2}}} \right) \left( 1+\mathrm{j} \, \frac{f}{f_{\mathrm{H3}}} \right)}
$$
where $f_{\mathrm{H1}}=1 \, \mathrm{MHz}$, $f_{\mathrm{H2}}=10 \, \mathrm{MHz}$, $f_{\mathrm{H3}}=50 \, \mathrm{MHz}$. If this operational amplifier is used to form a resistive negative feedback amplifier circuit, and a phase margin of 45° is required, what is the maximum loop gain of this amplifier circuit?

Options:
A. $$
1 7 ~ \mathrm{d B}
$$
B. $$
2 0 ~ \mathrm{d B}
$$
C. $$
2 1 ~ \mathrm{d B}
$$
D. $$
2 5 ~ \mathrm{d B}
$$
E. $$
1 8 ~ \mathrm{d B}
$$
F. $$
1 0 ~ \mathrm{d B}
$$
G. $$
1 2 ~ \mathrm{d B}
$$
H. $$
2 2 ~ \mathrm{d B}
$$
I. $$
1 5 ~ \mathrm{d B}
$$
J. $$
2 8 ~ \mathrm{d B}
$$
Answer: E
A coil is connected in series with a variable capacitor $C$ and a thermoelectric milliammeter with an internal resistance of 20Ω. The system is connected to an oscillator with a constant output amplitude and variable frequency. When the capacitance is set to 0.2μF and the frequency is adjusted to 10/π kHz, the circuit resonates. If the capacitor $C$ remains unchanged at 0.2μF and the frequency is altered, when the frequency is at 9.2/π kHz, the current reading drops to $1 / \sqrt{2}$ of the resonance value. Then, connect the capacitor in parallel with the coil, readjust the oscillator frequency to cause resonance in the circuit, assume the oscillator's output voltage amplitude is 5V (RMS), the resonant frequency and the milliammeter reading are ().

Options:
A. $$
\frac{9 0} {\pi} \times1. 0 0 0 3 4 \mathrm{k H z}, \ \ 4. 2 9 5 \mathrm{m A}
$$
B. $$
\frac{1 0} {\pi} \times1. 0 2 0 3 4 \mathrm{k H z}, \ \ 3. 2 9 5 \mathrm{m A}
$$
C. $$
\frac{1 0} {\pi} \times1. 0 0 0 3 4 \mathrm{k H z}, \ \ 3. 6 9 5 \mathrm{m A}
$$
D. $$
\frac{1 1} {\pi} \times1. 0 0 0 3 4 \mathrm{k H z}, \ \ 3. 5 9 5 \mathrm{m A}
$$
E. $$
\frac{1 0} {\pi} \times1. 0 0 0 3 4 \mathrm{k H z}, \ \ 3. 2 9 9 \mathrm{m A}
$$
F. $$
\frac{1 0} {\pi} \times1. 0 0 0 3 6 \mathrm{k H z}, \ \ 3. 2 9 5 \mathrm{m A}
$$
G. $$
\frac{1 0} {\pi} \times1. 0 0 0 3 8 \mathrm{k H z}, \ \ 3. 2 9 5 \mathrm{m A}
$$
H. $$
\frac{1 0} {\pi} \times1. 0 0 0 3 4 \mathrm{k H z}, \ \ 3. 2 9 5 \mathrm{m A}
$$
I. $$
\frac{1 0} {\pi} \times1. 0 0 1 3 4 \mathrm{k H z}, \ \ 2. 2 9 5 \mathrm{m A}
$$
J. $$
\frac{1 0} {\pi} \times0. 9 0 0 3 4 \mathrm{k H z}, \ \ 3. 2 9 5 \mathrm{m A}
$$
Answer: H
A signal $A \operatorname{cos} \omega_{\epsilon} t$ suffers additional interference from another signal $N \operatorname{cos} (\omega_s + \omega_{N}) t$. If $A \gg N$, the frequency offset of the combined signal is ().

Options:
A. $$
A \ \omega_{\epsilon} / 2 \pi A=A f_{\epsilon} / A
$$
B. $$
N \ \omega_{\epsilon} / 2 \pi N=N f_{\epsilon} / N
$$
C. $$
N \ \omega_{\epsilon} / 2 \pi A=N f_{\epsilon} / A
$$
D. $$
A \ \omega_{N} / 2 \pi N=A f_{N} / N
$$
E. $$
N \ \omega_{s} / 2 \pi A=N f_{s} / A
$$
F. $$
N \ \omega_{s} / 2 \pi N=N f_{s} / N
$$
G. $$
A \ \omega_{N} / 2 \pi A=A f_{N} / A
$$
H. $$
N \ \omega_{N} / 2 \pi A=N f_{N} / A
$$
I. $$
A \ \omega_{s} / 2 \pi N=A f_{s} / N
$$
J. $$
A \ \omega_{s} / 2 \pi A=A f_{s} / A
$$
Answer: H
What is the percentage of the total power contained in the sidebands of the frequency-modulated wave $u=A \cos (\omega_\epsilon t + 5 \cos \omega_{M} t)$ ?

Options:
A. 48.90%
B. 67.20%
C. 34.15%
D. 91.45%
E. 59.30%
F. 57.65%
G. 72.05%
H. 83.60%
I. 96.85%
J. 52.75%
Answer: I
The estimated bandwidth required for generating a 5 rad phase shift by a 5 kHz signal at 100 MHz is ().

Options:
A. 150kHz
B. 200kHz
C. 600kHz
D. 10kHz
E. 300kHz
F. 40kHz
G. 60kHz
H. 70kHz
I. 50kHz
J. 500kHz
Answer: G
Transmit a band-limited signal of $3.9 \sim 8.9 \text{ kHz}$ as a PAM waveform, and the minimum required sampling frequency is ().

Options:
A. 17.8kHz
B. 18.6kHz
C. 15.8kHz
D. 20.8kHz
E. 12.8kHz
F. 16.4kHz
G. 19.2kHz
H. 21.0kHz
I. 13.2kHz
J. 14.5kHz
Answer: A
A 5kHz signal needs to be transmitted using PCM (Pulse Code Modulation). If the signal-to-noise ratio at the receiver's input must be at least 50dB, and assuming that there is no error caused by thermal noise in the receiver, what is the estimated the required minimum number of quantization levels?

Options:
A. 11MHz,1024
B. 14kHz,1024
C. 8MHz,768
D. 7MHz,64
E. 5kHz,1024
F. 9MHz,512
G. 12MHz,256
H. 15kHz,256
I. 6kHz,128
J. 10MHz,512
Answer: J
Three identical dipoles forming a linear antenna array are spaced 1/4 $\lambda$ apart and are oriented perpendicular to the horizontal plane. Each dipole is fed with a current of equal amplitude, but there is a phase lag of $\delta$ radians between adjacent elements. In the horizontal plane, the radiation pattern of the dipoles is omnidirectional. The input impedance of each dipole is determined using the antenna's self-impedance and mutual impedance.Assuming the feed current has an effective value of 5A, with $\delta = 1/2 \pi$, ${\bf Z}_{11} = 75 \Omega$, ${\bf Z}_{12} = - (10 + j 20) \Omega$, and ${\bf Z}_{13} = (5 + j 10) \Omega$, what is the total radiated power?

Options:
A. 1600W
B. 3650W
C. 7300W
D. 1200W
E. 4200W
F. 5600W
G. 5000W
H. 8100W
I. 6500W
J. 2500W
Answer: G
A linear antenna array composed of four identical units is fed with a progressive phase lag of $\delta$ radians. The currents have amplitudes of $I$, $3I$, $3I$, and $I$. Each unit is spaced $d$ meters apart, and all units have an omnidirectional radiation pattern in the horizontal plane. What is the beamwidth under the condition where $d=0.35\lambda$?

Options:
A. 48°,100°
B. 54°,110°
C. 60°,120°
D. 58°,112°
E. 67°,130°
F. 53°,108°
G. 55°,113°
H. 51°,105°
I. 70°,115°
J. 62°,118°
Answer: B
There is a crane which, when lifting cargo, experiences impact vibrations, followed by gradually diminishing vibrations. The maximum amplitude resulting from the impact is measured to be 10 mm, with a period $T=0.04$ s. Assuming the system's relative damping coefficient is $\xi=0.02$. Calculate the time required for the amplitude to decay to 0.5 mm.

Options:
A. $$
9. 8 5 3 \mathrm{s}
$$
B. $$
9. 5 6 3 \mathrm{s}
$$
C. $$
9. 5 3 4 \mathrm{s}
$$
D. $$
8. 5 3 4 \mathrm{s}
$$
E. $$
9. 5 4 4 \mathrm{s}
$$
F. $$
9. 5 3 9 \mathrm{s}
$$
G. $$
9. 5 2 4 \mathrm{s}
$$
H. $$
9. 7 5 4 \mathrm{s}
$$
I. $$
7. 5 3 4 \mathrm{s}
$$
J. $$
9. 0 3 4 \mathrm{s}
$$
Answer: C
Two shafts made of the same material, with the same cross-sectional area and length, have different cross-section shapes: one is circular, and the other is square. If the torque ($M$) applied at the end of the shafts is also the same, calculate the maximum shear stress and torsional deformation for the two shafts.(assume that the diameter of the circular cross-section axle is d, and the side length of the square cross-section axle is a.)

Options:
A. $$
\frac{1 8 M} {\pi d^{3}}
$$
$$
\frac{3 4 M l} {G \pi d^{4}}
$$
$$
\frac{M} {0. 2 1 5 a^{2}}
$$
$$
\frac{M l} {0. 1 4 5 G a^{4}}
$$
B. $$
\frac{1 5 M} {\pi d^{5}}
$$
$$
\frac{2 8 M l} {G \pi d^{2}}
$$
$$
\frac{M} {0. 2 1 2 a^{4}}
$$
$$
\frac{M l} {0. 1 4 2 G a^{4}}
$$
C. $$
\frac{1 4 M} {\pi d^{2}}
$$
$$
\frac{2 5 M l} {G \pi d^{5}}
$$
$$
\frac{M} {0. 2 1 0 a^{4}}
$$
$$
\frac{M l} {0. 1 3 8 G a^{3}}
$$
D. $$
\frac{1 0 M} {\pi d^{3}}
$$
$$
\frac{3 6 M l} {G \pi d^{4}}
$$
$$
\frac{M} {0. 2 0 4 a^{3}}
$$
$$
\frac{M l} {0. 1 3 6 G a^{4}}
$$
E. $$
\frac{1 3 M} {\pi d^{4}}
$$
$$
\frac{2 9 M l} {G \pi d^{3}}
$$
$$
\frac{M} {0. 2 1 1 a^{2}}
$$
$$
\frac{M l} {0. 1 4 7 G a^{3}}
$$
F. $$
\frac{1 2 M} {\pi d^{2}}
$$
$$
\frac{3 0 M l} {G \pi d^{3}}
$$
$$
\frac{M} {0. 2 0 5 a^{3}}
$$
$$
\frac{M l} {0. 1 4 0 G a^{4}}
$$
G. $$
\frac{1 6 M} {\pi d^{3}}
$$
$$
\frac{3 2 M l} {G \pi d^{4}}
$$
$$
\frac{M} {0. 2 0 8 a^{3}}
$$
$$
\frac{M l} {0. 1 4 1 G a^{4}}
$$
H. $$
\frac{2 0 M} {\pi d^{3}}
$$
$$
\frac{4 0 M l} {G \pi d^{2}}
$$
$$
\frac{M} {0. 2 1 8 a^{5}}
$$
$$
\frac{M l} {0. 1 6 0 G a^{3}}
$$
I. $$
\frac{1 9 M} {\pi d^{4}}
$$
$$
\frac{3 1 M l} {G \pi d^{3}}
$$
$$
\frac{M} {0. 2 0 7 a^{4}}
$$
$$
\frac{M l} {0. 1 4 8 G a^{2}}
$$
J. $$
\frac{1 7 M} {\pi d^{2}}
$$
$$
\frac{3 3 M l} {G \pi d^{4}}
$$
$$
\frac{M} {0. 2 0 9 a^{3}}
$$
$$
\frac{M l} {0. 1 3 9 G a^{3}}
$$
Answer: G
When the traffic at the entrance of a certain large bridge is busy, trucks are directed by traffic police to turn off the bridge. The average time for each truck to make the turn is 9 seconds. The traffic volume on the bridge is 300 vehicles per hour. Try to calculate the average time for the vehicles queued on the bridge to turn off the bridge is ().

Options:
A. 72s
B. 54s
C. 48s
D. 30s
E. 66s
F. 60s
G. 36s
H. 18s
I. 24s
J. 42s
Answer: G
A Jiefang brand truck has a rear axle load of $21.00 kN$ when empty and $59.97 kN$ when fully loaded. The wheel track is 1740 mm, with a center of gravity height of 663 mm when empty and 926 mm when fully loaded. Calculate the load transfer of the vehicle when fully loaded while traveling on a 30 m radius curve.

Options:
A. 31529N
B. 27891N
C. 20452N
D. 30205N
E. 29920N
F. 28875N
G. 31043N
H. 29991N
I. 23104N
J. 32560N
Answer: H
In a stream of traffic, 30% of the vehicles travel at a constant speed of $60 \mathrm{km/h}$, 30% at $80 \mathrm{km/h}$, and the remaining 40% at $100 \mathrm{km/h}$. An observation vehicle drives at a steady speed of $70 \mathrm{km/h}$ along with the traffic flow for 5 km, during which 17 vehicles overtake the observation vehicle. When the observation vehicle travels 5 km against the traffic flow at the same speed, it encounters 303 oncoming vehicles. What are the average speed and flow rate of the traffic stream?

Options:
A. 78km/h,2180veh/h
B. 85km/h,2560veh/h
C. 79km/h,2220veh/h
D. 82km/h,2240veh/h
E. 86km/h,2340veh/h
F. 83km/h,2380veh/h
G. 80km/h,2100veh/h
H. 75km/h,2300veh/h
I. 81km/h,2160veh/h
J. 84km/h,2400veh/h
Answer: D
On a certain two-way road, the traffic volumes in the two directions are 400 vehicles per hour and 600 vehicles per hour, respectively. What is the directional imbalance factor of this road?

Options:
A. 0.3
B. 0.2
C. 1.2
D. 0.9
E. 1.8
F. 0.6
G. 1.5
H. 2.0
I. 0.8
J. 0.4
Answer: F
Under conditions of axisymmetric deformation in a certain plane, the axial strain $\varepsilon_{z}$ is constant. Determine the expressions for the other two strain components $\varepsilon_{r}$ and $\varepsilon_{\theta}$ is (). (the material is incompressible).

Options:
A. $\varepsilon_{\theta} = -\frac{C\varepsilon_{z}}{r^{2}}; \quad \varepsilon_{r} = \frac{C\varepsilon_{z}}{r^{2}}$, where $C$ is a constant determined by the boundary conditions.
B. $\varepsilon_{\theta} = -\varepsilon_{z} + \frac{Cr}{2}; \quad \varepsilon_{r} = \varepsilon_{z} - \frac{Cr}{2}$, where $C$ is a constant determined by the boundary conditions.
C. $\varepsilon_{\theta} = \frac{\varepsilon_{z}}{3} + \frac{C}{r^{4}}; \quad \varepsilon_{r} = -\frac{\varepsilon_{z}}{3} + \frac{C}{r^{4}}$, where $C$ is a constant determined by the boundary conditions.
D. $\varepsilon_{\theta} = \frac{C}{r} - \varepsilon_{z} ; \quad \varepsilon_{r} = -\frac{C}{r} + \varepsilon_{z}$, where $C$ is a constant determined by the boundary conditions.
E. $\varepsilon_{\theta} = -2\varepsilon_{z} + \frac{C}{r^{3}}; \quad \varepsilon_{r} = 2\varepsilon_{z} - \frac{C}{r^{3}}$, where $C$ is a constant determined by the boundary conditions.
F. $\varepsilon_{\theta} = \varepsilon_{z} - \frac{C}{r^{3}}; \quad \varepsilon_{r} = -\varepsilon_{z} + \frac{C}{r^{3}}$, where $C$ is a constant determined by the boundary conditions.
G. $\varepsilon_{\theta} = -\frac{2\varepsilon_{z}}{3} + Cr; \quad \varepsilon_{r} = \frac{2\varepsilon_{z}}{3} - Cr$, where $C$ is a constant determined by the boundary conditions.
H. $\varepsilon_{\theta} = \frac{\varepsilon_{z}}{2} + \frac{C}{r^{2}}; \quad \varepsilon_{r} = -\frac{\varepsilon_{z}}{2} - \frac{C}{r^{2}}$, where $C$ is a constant determined by the boundary conditions.
I. $\varepsilon_{\theta} = -\frac{\varepsilon_{z}}{2} + \frac{C}{r^{2}}; \quad \varepsilon_{r} = -\frac{\varepsilon_{z}}{2} - \frac{C}{r^{2}}$, where $C$ is a constant determined by the boundary conditions.
J. $\varepsilon_{\theta} = \varepsilon_{z} + \frac{C}{r}; \quad \varepsilon_{r} = \varepsilon_{z} - \frac{C}{r}$, where $C$ is a constant determined by the boundary conditions.
Answer: I
The wall thickness of a certain pressure vessel is $h$, with a radius of $R$. The yield limit of the material used is $\sigma_s = 1000 \, \mathrm{N/mm}^2$, and the fracture toughness is $K_{1\mathrm{C}} = 1200 \, \mathrm{N \cdot mm^{-3/2}}$. Assume the vessel contains a through-thickness crack whose length is in the direction of the vessel axis, with a length of $2a = 3.8 \, \mathrm{mm}$. Determine the critical pressure $p_\mathrm{lc}$ at which the vessel will undergo catastrophic failure is ().

Options:
A. $$
5 0 2. 9 {\frac{h} {R}} \mathrm{N / m m}^{2}
$$
B. $$
4 1 0. 6 {\frac{R} {h}} \mathrm{N / m m}^{2}
$$
C. $$
4 9 1. 2 {\frac{R} {h}} \mathrm{N / m m}^{2}
$$
D. $$
3 8 4. 7 {\frac{R} {h}} \mathrm{N / m m}^{2}
$$
E. $$
4 8 9. 1 {\frac{h} {R}} \mathrm{N / m m}^{2}
$$
F. $$
4 9 1. 2 {\frac{h} {R}} \mathrm{N / m m}^{2}
$$
G. $$
3 9 4. 8 {\frac{h} {R}} \mathrm{N / m m}^{2}
$$
H. $$
4 9 8. 3 {\frac{h} {R}} \mathrm{N / m m}^{2}
$$
I. $$
4 6 0. 0 {\frac{R} {h}} \mathrm{N / m m}^{2}
$$
Answer: F
A multi-story brick building with reinforced concrete structural columns is set up.
For a multi-story brick house with reinforced concrete structural columns, which of the following propositions about the construction sequence of the walls best ensures the integrity of the walls?

Options:
A. Placing beams across the columns, installing plywood forms, mixing concrete, and assembling brick walls around.
B. Constructing timber frames, applying stucco finishes, securing roof tiles, and assembling brick facades.
C. Installing steel girders, mounting cement boards, applying waterproof membranes, and placing stone pavers.
D. Developing aluminum panels, setting up gypsum boards, pouring concrete foundations, and securing plaster coats.
E. Establishing a steel framework, erecting exterior walls, pouring cement floors, and securing masonry bricks.
F. Attaching drywall panels, using wooden studs, installing insulation, and setting exterior brick veneer.
G. Erecting scaffold structures, installing rubber gaskets, placing insulating layers, and finishing with vinyl siding.
H. Building exterior frames, attaching cladding panels, arranging roof trusses, and pouring concrete floors.
I. Tying reinforcement bars for the structural columns, laying brick walls, setting up formwork, and then pouring concrete structural columns.
J. Arranging concrete blocks, installing rebar grids, placing wooden templates, and securing metal plates.
Answer: I
A certain highway bridge is composed of multiple spans of simply supported beams, utilizing prestressed concrete box-section beams. The concrete strength grade of these box-section beams is C40, with an elastic modulus $E_{\mathrm{c}}=3.25 \times 10^{4} \mathrm{MPa}$. The cross-sectional area at mid-span of the box-section beam is $A = 5.3 \mathrm{m}^{2}$, and the moment of inertia is $I_{\mathrm{c}}=1.5 \mathrm{m}^{4}$. Try to determine which of the following values the impact coefficient $\mu$ for the highway Class-I vehicle lane load is closest to?
Hint: gravitational acceleration $g=10 \mathrm{m/s^{2}}$.

Options:
A. 0.24
B. 0.30
C. 0.26
D. 0.28
E. 0.22
F. 0.32
G. 0.35
H. 0.25
I. 0.18
J. 0.20
Answer: D
Under the condition of a temperature of 288K, allow the $\mathrm{NH}_{3}$ (Component A)-water (Component B) solution to be in contact with an organic liquid that is immiscible with water, with neither phase in motion. $\mathrm{NH_{3}}$ diffuses from the aqueous phase to the organic phase. At the two-phase interface, $\mathrm{NH}_{3}$ in the aqueous phase maintains an equilibrium composition with a value of 0.015 (mole fraction, same below), and the solution at this point has a density of $\rho_{1}=998.95 \, \mathrm{kg}/\mathrm{m}^{3}$. In the aqueous phase 3 mm away from the interface, the composition of $\mathrm{NH}_{3}$ is 0.08, and the solution at this point has a density of $\rho_{2}=997.12 \, \mathrm{kg}/\mathrm{m}^{3}$. At $288 \, \mathrm{K}$, the diffusion coefficient of $NH_3$ in water is $D = 1.77 \times 10^{-9} \, \mathrm{m}^{2}/\mathrm{s}$. Calculate the diffusion flux of $\mathrm{NH_{3}}$ under steady-state diffusion.

Options:
A. $$
2. 0 0 \times1 0^{-6} \, \mathrm{k m o l} / ( \mathrm{m}^{2} \, \cdot\, \mathrm{s} )
$$
B. $$
6. 9 0 \times1 0^{-7} \, \mathrm{k m o l} / ( \mathrm{m}^{2} \, \cdot\, \mathrm{s} )
$$
C. $$
8. 8 8 \times1 0^{-7} \, \mathrm{k m o l} / ( \mathrm{m}^{2} \, \cdot\, \mathrm{s} )
$$
D. $$
4. 0 8 \times1 0^{-5} \, \mathrm{k m o l} / ( \mathrm{m}^{2} \, \cdot\, \mathrm{s} )
$$
E. $$
2. 7 2 \times1 0^{-6} \, \mathrm{k m o l} / ( \mathrm{m}^{2} \, \cdot\, \mathrm{s} )
$$
F. $$
2. 2 4 \times1 0^{-6} \, \mathrm{k m o l} / ( \mathrm{m}^{2} \, \cdot\, \mathrm{s} )
$$
G. $$
5. 5 0 \times1 0^{-7} \, \mathrm{k m o l} / ( \mathrm{m}^{2} \, \cdot\, \mathrm{s} )
$$
H. $$
3. 1 5 \times1 0^{-6} \, \mathrm{k m o l} / ( \mathrm{m}^{2} \, \cdot\, \mathrm{s} )
$$
I. $$
1. 5 9 \times1 0^{-7} \, \mathrm{k m o l} / ( \mathrm{m}^{2} \, \cdot\, \mathrm{s} )
$$
J. $$
3. 3 3 \times1 0^{-6} \, \mathrm{k m o l} / ( \mathrm{m}^{2} \, \cdot\, \mathrm{s} )
$$
Answer: F
In the dryer, wet material is dried from a moisture content of 0.5 to 0.06 (both on a wet basis). Assume the dryer is an ideal dryer. Air is heated to the necessary temperature in the preheater and then sent into the dryer. When the air cools to 38°C in the dryer, it is reheated to 74°C using an intermediate heater. The conditions of the fresh moist air are known: temperature 25°C, humidity 0.005 kg/kg (bone-dry air); the conditions of the exhaust moist air are: temperature 38°C, humidity 0.034 kg/kg (bone-dry air). Calculate the amount of fresh moist air and the amount of heat required to dry 1000 kg of wet material.

Options:
A. $1.622×10^4kg$,$1.414×10^6kJ$
B. $1.580×10^4kg$,$1.380×10^6kJ$
C. $1.630×10^4kg$,$1.430×10^6kJ$
D. $1.700×10^4kg$,$1.450×10^6kJ$
E. $1.620×10^4kg$,$1.400×10^6kJ$
F. $1.610×10^4kg$,$1.410×10^6kJ$
G. $1.600×10^4kg$,$1.390×10^6kJ$
H. $1.500×10^4kg$,$1.300×10^6kJ$
I. $1.670×10^4kg$,$1.460×10^6kJ$
J. $1.640×10^4kg$,$1.420×10^6kJ$
Answer: A
Ammonia is absorbed using water in a packed tower. The operating pressure is 101.3 kPa, and the temperature is 298 K. Assuming the effective contact time of the liquid exposed to the gas at the surface of the packing is 0.01 s, and knowing that under the operating conditions the diffusion coefficient of ammonia in water is $D = 1.77 \times 10^{-9}$ m²/s, try applying the solute penetration model to calculate the average mass transfer coefficient $k_{\mathrm{cm}}$.

Options:
A. $$
5. 0 5 \times1 0^{-4} \, \mathrm{m / s}
$$
B. $$
4. 6 8 \times1 0^{-4} \, \mathrm{m / s}
$$
C. $$
5. 2 3 \times1 0^{-4} \, \mathrm{m / s}
$$
D. $$
5. 3 0 \times1 0^{-4} \, \mathrm{m / s}
$$
E. $$
4. 9 1 \times1 0^{-4} \, \mathrm{m / s}
$$
F. $$
4. 5 7 \times1 0^{-4} \, \mathrm{m / s}
$$
G. $$
3. 5 4 \times1 0^{-4} \, \mathrm{m / s}
$$
H. $$
4. 1 2 \times1 0^{-4} \, \mathrm{m / s}
$$
I. $$
3. 8 9 \times1 0^{-4} \, \mathrm{m / s}
$$
J. $$
4. 7 5 \times1 0^{-4} \, \mathrm{m / s}
$$
Answer: J
At 10°C and 101.3 kPa, the Henry's law constant for the $O_{2}-H_{2}O$ system is $3.31 \times 10^{6} \, \mathrm{kPa}$. Given that the phase equilibrium relationship conforms to Henry's law, determine the equilibrium concentration $c_{e}$, $x_{e}$, $X_{e}$ of $O_{2}$ in water after full contact with air at this temperature and pressure, as well as the phase equilibrium constant $m$ and the solubility coefficient $H$ of the system.

Options:
A. $$
c_{e}=2.5 8 4 \times1 0^{-4} \, \mathrm{k m o l} / m^{3} \,, \, \, \, \, X_{e} \approx x_{e}=5.6 7 2 \times1 0^{-4} \,, \, \, \, \, m=3.5 9 7 \times1 0^{4} \,, \, \, \, \, H=1. 6 3 8 \times1 0^{-5} \, \mathrm{k m o l} / m^{3}·kPa)
$$
B. $$
c_{e}=4.2 1 9 \times1 0^{-4} \, \mathrm{k m o l} / m^{3} \,, \, \, \, \, X_{e} \approx x_{e}=7.3 2 5 \times1 0^{-4} \,, \, \, \, \, m=2.6 8 1 \times1 0^{4} \,, \, \, \, \, H=1. 5 4 9 \times1 0^{-5} \, \mathrm{k m o l} / m^{3}·kPa)
$$
C. $$
c_{e}=4.2 7 9 \times1 0^{-4} \, \mathrm{k m o l} / m^{3} \,, \, \, \, \, X_{e} \approx x_{e}=7.1 3 8 \times1 0^{-4} \,, \, \, \, \, m=2.8 9 3 \times1 0^{4} \,, \, \, \, \, H=1. 7 5 4 \times1 0^{-5} \, \mathrm{k m o l} / m^{3}·kPa)
$$
D. $$
c_{e}=3.5 6 9 \times1 0^{-4} \, \mathrm{k m o l} / m^{3} \,, \, \, \, \, X_{e} \approx x_{e}=6.4 2 7 \times1 0^{-4} \,, \, \, \, \, m=3.2 6 7 \times1 0^{4} \,, \, \, \, \, H=1 .6 7 8 \times1 0^{-5} \, \mathrm{k m o l} / m^{3}·kPa)
$$
E. $$
c_{e}=3.3 0 2 \times1 0^{-4} \, \mathrm{k m o l} / m^{3} \,, \, \, \, \, X_{e} \approx x_{e}=6.0 8 3 \times1 0^{-4} \,, \, \, \, \, m=3.4 2 1 \times1 0^{4} \,, \, \, \, \, H=1. 8 7 4 \times1 0^{-5} \, \mathrm{k m o l} / m^{3}·kPa)
$$
F. $$
c_{e}=3.7 5 8 \times1 0^{-4} \, \mathrm{k m o l} / m^{3} \,, \, \, \, \, X_{e} \approx x_{e}=2.4 9 8 \times1 0^{-4} \,, \, \, \, \, m=3.1 2 3 \times1 0^{4} \,, \, \, \, \, H=1. 7 2 9 \times1 0^{-5} \, \mathrm{k m o l} / m^{3}·kPa)
$$
G. $$
c_{e}=4.9 3 7 \times1 0^{-4} \, \mathrm{k m o l} / m^{3} \,, \, \, \, \, X_{e} \approx x_{e}=7.0 6 5 \times1 0^{-4} \,, \, \, \, \, m=2.7 8 4 \times1 0^{4} \,, \, \, \, \, H=2. 4 1 2 \times1 0^{-5} \, \mathrm{k m o l} / m^{3}·kPa)
$$
H. $$
c_{e}=1.1 5 6 \times1 0^{-4} \, \mathrm{k m o l} / m^{3} \,, \, \, \, \, X_{e} \approx x_{e}=8.7 4 1 \times1 0^{-4} \,, \, \, \, \, m=3.6 4 2 \times1 0^{4} \,, \, \, \, \, H=1. 9 2 3 \times1 0^{-5} \, \mathrm{k m o l} / m^{3}·kPa)
$$
I. $$
c_{e}=3.6 2 5 \times1 0^{-4} \, \mathrm{k m o l} / m^{3} \,, \, \, \, \, X_{e} \approx x_{e}=4.8 7 2 \times1 0^{-4} \,, \, \, \, \, m=2.9 5 8 \times1 0^{4} \,, \, \, \, \, H=2. 3 5 1 \times1 0^{-5} \, \mathrm{k m o l} / m^{3}·kPa)
$$
J. $$
c_{e}=2.9 8 1 \times1 0^{-4} \, \mathrm{k m o l} / m^{3} \,, \, \, \, \, X_{e} \approx x_{e}=5.9 4 7 \times1 0^{-4} \,, \, \, \, \, m=3.7 4 1 \times1 0^{4} \,, \, \, \, \, H=1. 5 8 9 \times1 0^{-5} \, \mathrm{k m o l} / m^{3}·kPa)
$$
Answer: D
The silt from a certain harbor's sedimentation has properties of $\gamma=15.7 \, \mathrm{kN/m^{3}}$, $w=74\%$, and $d_{s}=2.70$. To clear the silt using a dredger, water must be used to mix the silt into a slurry with a 10% concentration (the soil particles make up 10% of the total mass of the slurry) before it can be transported. How much slurry, in terms of $\mathbf{m}^{3}$, must be transported to remove a total of 100 $\mathbf{km}^{3}$ of silt?

Options:
A. $$
7 5 0. 3 \times1 0^{3} {\mathrm{m}}^{3}
$$
B. $$
9 5 0. 1 \times1 0^{3} {\mathrm{m}}^{3}
$$
C. $$
8 9 2. 0 \times1 0^{3} {\mathrm{m}}^{3}
$$
D. $$
9 2 1. 7 \times1 0^{3} {\mathrm{m}}^{3}
$$
E. $$
7 8 4. 6 \times1 0^{3} {\mathrm{m}}^{3}
$$
F. $$
8 3 2. 9 \times1 0^{3} {\mathrm{m}}^{3}
$$
G. $$
8 4 5. 4 \times1 0^{3} {\mathrm{m}}^{3}
$$
H. $$
7 6 5. 2 \times1 0^{3} {\mathrm{m}}^{3}
$$
I. $$
8 1 0. 8 \times1 0^{3} {\mathrm{m}}^{3}
$$
J. $$
9 8 3. 5 \times1 0^{3} {\mathrm{m}}^{3}
$$
Answer: G
The volume of earthwork for a certain rolled earth dam is $2 \times 10^5 \mathrm{m}^3$, with a designed compacted dry density of $1.65 \mathrm{g/cm^3}$. The moisture content at the material site is 12.0%, with a natural density of $1.70 \mathrm{g/cm^3}$, a liquid limit of 32.0%, a plastic limit of 20.0%, and a particle relative density of 2.72. If the daily filling volume of the dam body is $3000 \mathrm{m}^3$, and the optimal moisture content of the soil is 95% of the plastic limit, how much water must be added each day to achieve the best compaction effect? To meet the needs of filling the earth dam, how much soil material must the material site have at a minimum?

Options:
A. $$
3 3 0. 6 t,
$$
$$
2. 1 9 0 {\times} 1 0^{5} {\bf m}^{3}
$$
B. $$
3 6 1. 1 t,
$$
$$
2. 2 0 5 {\times} 1 0^{5} {\bf m}^{3}
$$
C. $$
3 4 2. 2 t,
$$
$$
2. 1 5 0 {\times} 1 0^{5} {\bf m}^{3}
$$
D. $$
3 4 6. 5 t,
$$
$$
2. 1 7 4 {\times} 1 0^{5} {\bf m}^{3}
$$
E. $$
3 7 0. 4 t,
$$
$$
2. 0 5 0 {\times} 1 0^{5} {\bf m}^{3}
$$
F. $$
3 3 8. 8 t,
$$
$$
2. 3 0 0 {\times} 1 0^{5} {\bf m}^{3}
$$
G. $$
3 5 5. 5 t,
$$
$$
2. 2 2 5 {\times} 1 0^{5} {\bf m}^{3}
$$
H. $$
3 5 0. 0 t,
$$
$$
2. 0 9 0 {\times} 1 0^{5} {\bf m}^{3}
$$
I. $$
3 3 5. 9 t,
$$
$$
2. 1 6 0 {\times} 1 0^{5} {\bf m}^{3}
$$
J. $$
3 2 5. 2 t,
$$
$$
2. 2 5 0 {\times} 1 0^{5} {\bf m}^{3}
$$
Answer: D
The effective shear strength parameters of a certain saturated cohesive soil, measured by a consolidated undrained shear test, are $c^{\prime} = 20 \mathrm{kPa}$ and $\phi^{\prime} = 20^{\circ}.$ If a consolidated drained shear test is conducted on this soil sample with a confining pressure of $\sigma_{3} = 120 \mathrm{kPa}$, what additional deviatoric stress should be applied at failure?

Options:
A. $$
1 7 4. 6 \mathrm{k P a}
$$
B. $$
1 8 9. 0 \mathrm{k P a}
$$
C. $$
1 7 8. 3 \mathrm{k P a}
$$
D. $$
1 8 1. 8 \mathrm{k P a}
$$
E. $$
1 9 5. 2 \mathrm{k P a}
$$
F. $$
1 8 3. 9 \mathrm{k P a}
$$
G. $$
1 6 9. 4 \mathrm{k P a}
$$
H. $$
1 6 5. 7 \mathrm{k P a}
$$
I. $$
1 7 1. 1 \mathrm{k P a}
$$
J. $$
1 9 2. 5 \mathrm{k P a}
$$
Answer: D
A gravity retaining wall is 6.1 meters high, with a vertical, smooth back, and a level backfill surface. The backfill consists of medium sand, with an internal friction angle of 30° and a unit weight of $17.3\mathrm{kN/m^{3}}$. Try using the wedge method to calculate the magnitude of the resultant active earth pressure is().

Options:
A. $$
1 2 0. 1 \mathbf{k N} / \mathbf{m}
$$
B. $$
1 1 5. 9 \mathbf{k N} / \mathbf{m}
$$
C. $$
1 0 5. 8 \mathbf{k N} / \mathbf{m}
$$
D. $$
1 0 4. 3 \mathbf{k N} / \mathbf{m}
$$
E. $$
1 1 2. 8 \mathbf{k N} / \mathbf{m}
$$
F. $$
1 0 7. 2 \mathbf{k N} / \mathbf{m}
$$
G. $$
9 8. 6 \mathbf{k N} / \mathbf{m}
$$
H. $$
1 1 0. 5 \mathbf{k N} / \mathbf{m}
$$
I. $$
1 0 3. 5 \mathbf{k N} / \mathbf{m}
$$
J. $$
1 2 3. 7 \mathbf{k N} / \mathbf{m}
$$
Answer: F
The purpose of pre-sowing irrigation is to ensure that the soil moisture content at the time of sowing meets the needs for germination and to supply the water required for evaporation and transpiration during the seedling stage. Additionally, it aims to store sufficient water within the maximum planned moisture layer for use once the crop roots grow deeper.
Basic Data
(1) Maximum planned moisture layer of the soil $\mathrm{H=0.8 \, m}$.
(2) Average soil porosity $n=41.3 \%$ (as a percentage of the soil volume).
(3) Field capacity of the soil $\theta_{\text{max}}=75.0\%$ (as a percentage of the pore volume).
(4) Natural soil moisture content before sowing, $\theta_0=48.0\%$ (as a percentage of the pore volume).
The pre-sowing irrigation quota is ().

Options:
A. $5 8. 0 \mathrm{m}^{3}$ per mu
B. $6 2. 3 \mathrm{m}^{3}$ per mu
C. $5 9. 4 \mathrm{m}^{3}$ per mu
D. $6 3. 7 \mathrm{m}^{3}$ per mu
E. $5 9. 6 \mathrm{m}^{3}$ per mu
F. $5 7. 5 \mathrm{m}^{3}$ per mu
G. $5 9. 5 \mathrm{m}^{3}$ per mu
H. $6 1. 2 \mathrm{m}^{3}$ per mu
I. $6 0. 0 \mathrm{m}^{3}$ per mu
J. $5 8. 9 \mathrm{m}^{3}$ per mu
Answer: G
The radius of the Moon's orbit around the Earth is approximately 60 times the Earth's radius, with an orbital period of about 27 days. Using Kepler's laws, calculate: at what altitude above the Earth's surface within the equatorial plane can a man-made satellite orbit along with the Earth, as if it were motionless in the sky?

Options:
A. $$
2. 5 8 {\times} 1 0^{4} k m
$$
B. $$
3. 6 3 {\times} 1 0^{4} k m
$$
C. $$
5. 1 9 {\times} 1 0^{4} k m
$$
D. $$
8. 0 5 {\times} 1 0^{4} k m
$$
E. $$
4. 4 2 {\times} 1 0^{4} k m
$$
F. $$
6. 6 6 {\times} 1 0^{4} k m
$$
G. $$
4. 7 2 {\times} 1 0^{4} k m
$$
H. $$
5. 8 7 {\times} 1 0^{4} k m
$$
I. $$
7. 3 9 {\times} 1 0^{4} k m
$$
J. $$
1. 4 3 {\times} 1 0^{4} k m
$$
Answer: B
The "Mir" space station has a total mass of 137t and a working volume exceeding $400 m^{2}$, making it the largest spacecraft humanity has launched into space for exploration, earning the nickname "Artificial Heavenly Palace." This "colossal entity" in space made its first-ever precise descent into a predetermined sea area according to ground instructions, marking a historic event for humankind. During its normal operation, the average altitude of the "Mir" space station was approximately 350km above ground. To ensure its eventual safe demise, the Russian Space Agency's control center meticulously planned and managed the station's descent. Prior to crashing, the space station entered a designated low orbit, at which point its altitude was approximately 240km above the ground. As "Mir" traveled along this specified low orbit, its average orbital altitude decreased by 2.7km every day.
Suppose the "Mir" space station typically orbited in a circular path with an altitude of $350 \mathrm{km}$ and descended along a designated circular low orbit at an altitude of $240 \mathrm{km}$ before finally falling. During this designated low orbit, the station's altitude changes insignificantly with each orbit, allowing calculations to treat its motion for each orbit as uniform circular motion.
During one complete orbit along the specified low orbit, how much does the space station's altitude change on average? (Use Earth's radius $R=6.4 \times 10^{3} \mathrm{km}$, and keep one significant figure in the calculation.)

Options:
A. $$
-3. 1 \mathrm{k m}
$$
B. $$
-2. 7 \mathrm{k m}
$$
C. $$
-5. 8 \mathrm{k m}
$$
D. $$
-2. 9 \mathrm{k m}
$$
E. $$
-3. 3 \mathrm{k m}
$$
F. $$
-3. 0 \mathrm{k m}
$$
G. $$
-2. 5 \mathrm{k m}
$$
H. $$
-3. 2 \mathrm{k m}
$$
I. $$
-2. 4 \mathrm{k m}
$$
J. $$
-2. 3 \mathrm{k m}
$$
Answer: B
The spacecraft is accelerating vertically upward at a constant acceleration of $g / 2$. Inside the spacecraft, a spring scale measures the weight of an object with a mass of $10 \mathrm{kg}$ as $7.5 \mathrm{N}$. Given that the Earth's radius is $6400 \mathrm{km}$, find the height of the spacecraft above the ground at the time of measurement. ($g$ is the gravitational acceleration at the Earth's surface.)

Options:
A. 2950km
B. 12800km
C. 6400km
D. 3200km
E. 4800km
F. 8000km
G. 1600km
H. 9600km
I. 7200km
J. 5600km
Answer: C
A photon with a wavelength of $\lambda$ is emitted from the surface of the Sun. Calculate the redshift $\Delta\lambda$ of the wavelength of this photon when it reaches the surface of the Earth. (The mass and radius of the Sun are $1.99 ×10^{30}$ kg and $6.96×10^{8}$ m, respectively; the mass and radius of the Earth are $5.98 ×10^{24}$ kg and $6.37×10^{6}$ m, respectively.)

Options:
A. $$
2. 9 0 \times1 0^{-5} \,
$$
B. $$
1. 2 6 \times1 0^{-5} \,
$$
C. $$
9. 8 7 \times1 0^{-9} \,
$$
D. $$
3. 4 5 \times1 0^{-6} \,
$$
E. $$
4. 1 3 \times1 0^{-8} \,
$$
F. $$
7. 4 1 \times1 0^{-7} \,
$$
G. $$
5. 3 0 \times1 0^{-6} \,
$$
H. $$
5. 0 0 \times1 0^{-7} \,
$$
I. $$
1. 7 8 \times1 0^{-6} \,
$$
J. $$
2. 1 2 \times1 0^{-6} \,
$$
Answer: J
The solar luminosity is measured at $3.9 \times 10^{26} \mathrm{~ W}$. It generates energy from the thermonuclear fusion reactions that convert hydrogen into helium, releasing 26 MeV of energy for each helium nucleus formed. If the Sun's output power remains at the above value unchanged for $500$ million years, what is the mass fraction of helium inside the Sun?

Options:
A. 6%
B. 9%
C. 5.8%
D. 4.2%
E. 8%
F. 10%
G. 5%
H. 4.5%
I. 3.8%
J. 7%
Answer: G
In the infrared band, a star has been observed orbiting a massive yet invisible object (a black hole) at the center of the Milky Way. The center of the Milky Way is identified as Sagittarius A* (Sgr A*), which is a compact source of radio and X-rays (see "Physics Today" from February 2003). The elliptical orbit has a period of 15 years, an eccentricity of 0.87, and the closest distance to the center of the galaxy (periastron) is approximately 17 light-hours. Calculate the orbital velocity of the star at the periastron.

Options:
A. $$
4 \ 7 0 0 \ \mathrm{k m / s}
$$
B. $$
7 \ 9 0 0 \ \mathrm{k m / s}
$$
C. $$
7 \ 1 7 0 \ \mathrm{k m / s}
$$
D. $$
5 \ 1 7 0 \ \mathrm{k m / s}
$$
E. $$
9 \ 3 0 0 \ \mathrm{k m / s}
$$
F. $$
3 \ 9 5 0 \ \mathrm{k m / s}
$$
G. $$
8 \ 2 2 0 \ \mathrm{k m / s}
$$
H. $$
6 \ 4 0 0 \ \mathrm{k m / s}
$$
I. $$
2 \ 8 4 0 \ \mathrm{k m / s}
$$
J. $$
6 \ 3 5 0 \ \mathrm{k m / s}
$$
Answer: C
The angular deviation caused by a photon passing by a particle $M$ according to Newtonian mechanics is__. (Express the result in a form that includes the term $b$, where $b$ is the closest distance of approach.)

Options:
A. $$\quad\Delta\theta=2 G M / (b c^{3})$$
B. $$\quad\Delta\theta=2 G M / (b^{2} c)$$
C. $$\quad\Delta\theta=G M / (b c^{2})$$
D. $$\quad\Delta\theta=G M / (2 b c^{2})$$
E. $$\quad\Delta\theta=2 G M / (b c^{2})$$
F. $$\quad\Delta\theta=3 G M / (b c^{2})$$
G. $$\quad\Delta\theta=2 G / (b M c^{2})$$
H. $$\quad\Delta\theta=G M b / (2 c^{2})$$
I. $$\quad\Delta\theta=G b / (2 M c^{2})$$
J. $$\quad\Delta\theta=4 G M / (b c^{2})$$
Answer: E
The known surface temperature of the Sun is $5,780 \ \mathrm{K}$, with a radius of $7 \times 10^{8} \ \mathrm{m}$. The Sun's energy is provided by the fusion of hydrogen into helium. If 5% of the Sun's hydrogen has currently fused into helium, and the Sun's luminosity remains constant, the age of the Sun is__.

Options:
A. 6 million years
B. 9 million years
C. 2 billion years
D. 7 trillion years
E. 3 billion years
F. 1 million years
G. 8 billion years
H. 5 billion years
I. 4 million years
J. 12 billion years
Answer: H
Particle $A$ moves at a constant speed $v_{0}$ along the circumference $x^{2}+y^{2}=R^{2}, \; z= a$. It drives particle $B$ to slide along the line $x= b, \; z=0$ using a rod of length $l$.What is the velocity of particle $B$ ?

Options:
A. $v_0\sin\varphi+\frac{(R\cos\varphi-b)v_0\cos\varphi}{\sqrt{l^2-a^2-(R\cos\varphi-b)^2}}.$
B. $v_0\cos\theta-\frac{(R\cos\theta-b)v_0\sin\theta}{\sqrt{l^2-a^2-(R\cos\theta-b)^2}}.$
C. $v_0\cos\varphi-\frac{(R\sin\varphi-b)v_0\cos\varphi}{\sqrt{l^2-a^2-(R\sin\varphi-b)^2}}.$
D. $v_0\sin\theta-\frac{(R\sin\theta-b)v_0\cos\theta}{\sqrt{l^2-a^2-(R\sin\theta-b)^2}}.$
E. $v_0\cos\psi-\frac{(R\cos\psi-b)v_0\sin\psi}{\sqrt{l^2-a^2-(R\cos\psi-b)^2}}.$
F. $v_0\cos\varphi-\frac{(R\cos\varphi-b)v_0\sin\varphi}{\sqrt{l^2-a^2-(R\cos\varphi-b)^2}}.$
G. $v_0\cos\varphi+\frac{(R\sin\varphi-b)v_0\sin\varphi}{\sqrt{l^2-a^2-(R\sin\varphi-b)^2}}.$
H. $v_0\sin\psi-\frac{(R\sin\psi-b)v_0\cos\psi}{\sqrt{l^2-a^2-(R\sin\psi-b)^2}}.$
I. $v_0\sin\varphi-\frac{(R\sin\varphi-b)v_0\cos\varphi}{\sqrt{l^2-a^2-(R\sin\varphi-b)^2}}.$
J. $v_0\sin\varphi-\frac{(R\cos\varphi-b)v_0\cos\varphi}{\sqrt{l^2-a^2-(R\cos\varphi-b)^2}}.$
Answer: F
Given that the trajectory of a particle under the influence of a central force is a spiral $r = k \theta^{2},$ where $k$ is a constant.What is the expression for the central force $F(r)$ ?

Options:
A. $F=-mh^2\left(\frac{7k}{r^5}+\frac2{r^6}\right).$
B. $F=-mh^2\left(\frac{4k}{r^5}+\frac1{r^2}\right).$
C. $F=-mh^2\left(\frac{k}{r^2}+\frac2{r^4}\right).$
D. $F=-mh^2\left(\frac{9k}{r^3}+\frac1{r^2}\right).$
E. $F=-mh^2\left(\frac{3k}{r^6}+\frac2{r^5}\right).$
F. $F=-mh^2\left(\frac{k}{r^3}+\frac1{r^5}\right).$
G. $F=-mh^2\left(\frac{5k}{r^3}+\frac2{r^4}\right).$
H. $F=-mh^2\left(\frac{2k}{r^4}+\frac3{r^3}\right).$
I. $F=-mh^2\left(\frac{6k}{r^4}+\frac1{r^3}\right).$
J. $F=-mh^2\left(\frac{8k}{r^2}+\frac1{r^6}\right).$
Answer: I
A particle with mass $m$ moves along the ellipse $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$. The particle's acceleration is parallel to the $y$-axis when $t=0$. At this time, the particle's coordinates are: $x=0, y=b$, and the initial velocity is $v_{0}$.What is the force acting on the particle at every point along its trajectory ?

Options:
A. $$
F_{y}=-m \frac{v_{0}^{2} b^{4}} {a^{2} y^{3}}.
$$
B. $$
F_{y}=-\frac{m v_{0} b^{4}} {a^{2} y v}.
$$
C. $$
F_{y}=-\frac{m v_{0}^{2} b^{2}} {a y^{3}}.
$$
D. $$
F_{y}=m \frac{v_{0}^{2} a^{2} b^{4}} {y^{3} x}.
$$
E. $$
F_{y}=-m \frac{b^{4} v_{0}^{2}} {y^{3} x a^{2}}.
$$
F. $$
F_{y}=-m \frac{v_{0}^{2} a^{4}} {b^{2} y^{3}}.
$$
G. $$
F_{y}=m \frac{v_{0}^{2} b^{4}} {a^{2} x^{3}}.
$$
H. $$
F_{y}=\frac{m v_{0}^{2} a^{4}} {b^{2} x^{3}}.
$$
I. $$
F_{y}=m \frac{v_{0}^2 b^{4}} {a y^{4}}.
$$
J. $$
F_{y}=\frac{-m b^{4} v_{0}^{2}} {a y^{2}}.
$$
Answer: A
A bullet with a mass of $20 \ \mathrm{g}$ is fired from the gun barrel at a speed of $v=650 \ \mathrm{m/s}$, traveling through the barrel for $t=0.00095$ seconds. Assuming the cross-sectional area of the barrel is $\sigma=150 \ \mathrm{mm}^{2}$.What is the average pressure of the gas required to fire the bullet ?

Options:
A. $$
7. 0 8 \times1 0^{4} \mathrm{~ N / m m^{2} ~}.
$$
B. $$
9. 1 2 \times1 0^{4} \mathrm{~ N / m m^{2} ~}.
$$
C. $$
8. 1 4 \times1 0^{4} \mathrm{~ N / m m^{2} ~}.
$$
D. $$
1. 5 3 \times1 0^{4} \mathrm{~ N / m m^{2} ~}.
$$
E. $$
1. 2 9 \times1 0^{4} \mathrm{~ N / m m^{2} ~}.
$$
F. $$
1. 6 7 \times1 0^{4} \mathrm{~ N / m m^{2} ~}.
$$
G. $$
7. 9 3 \times1 0^{4} \mathrm{~ N / m m^{2} ~}.
$$
H. $$
6. 6 4 \times1 0^{4} \mathrm{~ N / m m^{2} ~}.
$$
I. $$
1. 0 5 \times1 0^{4} \mathrm{~ N / m m^{2} ~}.
$$
J. $$
8. 7 0 \times1 0^{4} \mathrm{~ N / m m^{2} ~}.
$$
Answer: B
The mass of the steam hammer is 12 t, and it falls onto the anvil block at a speed of 5 m/s. The combined mass of the anvil block and the forging is 250 t. Determine the work absorbed by the forging $A_{1}$, the work consumed by the foundation vibration $A_{2}$.What is the efficiency of the steam hammer $\eta$? Assume the collision is perfectly plastic.

Options:
A. $$
A_{1}=1 4 0 ~ \mathrm{k N} \cdot\mathrm{m}, ~ ~ A_{2}=7. 2 0 ~ \mathrm{k N} \cdot\mathrm{m}, ~ ~ \eta=0. 9 0.
$$
B. $$
A_{1}=1 4 4 ~ \mathrm{k N} \cdot\mathrm{m}, ~ ~ A_{2}=6. 8 2 ~ \mathrm{k N} \cdot\mathrm{m}, ~ ~ \eta=0. 9 2.
$$
C. $$
A_{1}=1 3 9 ~ \mathrm{k N} \cdot\mathrm{m}, ~ ~ A_{2}=7. 1 0 ~ \mathrm{k N} \cdot\mathrm{m}, ~ ~ \eta=0. 9 7.
$$
D. $$
A_{1}=1 4 8 ~ \mathrm{k N} \cdot\mathrm{m}, ~ ~ A_{2}=6. 9 5 ~ \mathrm{k N} \cdot\mathrm{m}, ~ ~ \eta=0. 9 6.
$$
E. $$
A_{1}=1 3 5 ~ \mathrm{k N} \cdot\mathrm{m}, ~ ~ A_{2}=7. 3 5 ~ \mathrm{k N} \cdot\mathrm{m}, ~ ~ \eta=0. 9 4.
$$
F. $$
A_{1}=1 5 2 ~ \mathrm{k N} \cdot\mathrm{m}, ~ ~ A_{2}=6. 5 5 ~ \mathrm{k N} \cdot\mathrm{m}, ~ ~ \eta=0. 8 5.
$$
G. $$
A_{1}=1 4 3 ~ \mathrm{k N} \cdot\mathrm{m}, ~ ~ A_{2}=6. 8 7 ~ \mathrm{k N} \cdot\mathrm{m}, ~ ~ \eta=0. 9 5.
$$
H. $$
A_{1}=1 3 7 ~ \mathrm{k N} \cdot\mathrm{m}, ~ ~ A_{2}=7. 0 1 ~ \mathrm{k N} \cdot\mathrm{m}, ~ ~ \eta=0. 9 1.
$$
I. $$
A_{1}=1 5 0 ~ \mathrm{k N} \cdot\mathrm{m}, ~ ~ A_{2}=5. 9 0 ~ \mathrm{k N} \cdot\mathrm{m}, ~ ~ \eta=0. 8 8.
$$
J. $$
A_{1}=1 4 5 ~ \mathrm{k N} \cdot\mathrm{m}, ~ ~ A_{2}=6. 7 5 ~ \mathrm{k N} \cdot\mathrm{m}, ~ ~ \eta=0. 9 3.
$$
Answer: G
Calculate the annual consumption of natural uranium in a nuclear power plant with a power output of 1 million watts. If the fuel utilization rate is 3.5 kg/ton, and the heat released per kilogram of fissile material is $\mathbf{1.6 \times 10^{10}}$ kilocalories, the power plant operates 7,000 hours per year, with an efficiency of 0.25.

Options:
A. $$
431 tons/year
$$
B. $$
456 tons/year
$$
C. $$
395 tons/year
$$
D. $$
410 tons/year
$$
E. $$
475 tons/year
$$
F. $$
442 tons/year
$$
G. $$
520 tons/year
$$
H. $$
463 tons/year
$$
I. $$
389 tons/year
$$
J. $$
498 tons/year
$$
Answer: A
The average atomic number of elements contained in the main parts of the human body is very close to the average atomic number of air. If a dose of 1 roentgen is equivalent to 1 cm$^{3}$ of air absorbing 0.11 erg of energy, then how much energy is absorbed by 1 cm$^{3}$ of tissue in the human body at this dose? The density of the human body is 0.924 g/cm$^{3}$.

Options:
A. 58.7 Erg
B. 71.3 Erg
C. 66.9 Erg
D. 45.2 Erg
E. 53.4 Erg
F. 78.6 Erg
G. 89.7 Erg
H. 62.8 Erg
I. 84.5 Erg
J. 95.1 Erg
Answer: F
To reduce the intensity of the thermal neutron flux to 0.1% of its original value, what should be the thickness of the cadmium layer? (The effective cross-section of cadmium is 2900 barns.) A fast neutron flux passes through graphite before hitting a planar absorber made of boron $(\sigma=703 \text{ barns})$. When passing through the absorber, the neutron flux intensity decreases by 50%. What is the required thickness of the boron absorber?

Options:
A. $$
0.03 centimeters
$$
B. $$
0.10 centimeters
$$
C. $$
0.09 centimeters
$$
D. $$
0.05 centimeters
$$
E. $$
0.07 centimeters
$$
F. $$
0.12 centimeters
$$
G. $$
0.15 centimeters
$$
H. $$
0.06 centimeters
$$
I. $$
0.08 centimeters
$$
J. $$
0.04 centimeters
$$
Answer: D
Pour 5 liters of oil into the engine's oil reservoir. After operating for a certain period, take out 1 milliliter of oil and measure its radioactivity using a Geiger counter, registering 50 pulses per minute. Given that the specific radioactivity of irradiated rings is 10 pulses per minute per gram, what is the percentage of wear on the rings?

Options:
A. 0.30%
B. 0.20%
C. 0.75%
D. 0.50%
E. 1.00%
F. 0.60%
G. 0.05%
H. 0.10%
I. 0.25%
J. 0.40%
Answer: I
An atom that does not have a permanent magnetic moment is called a diamagnetic atom. If we ignore the spin of the electron, find the induced magnetic moment produced by a weak magnetic field $B$ acting on a ground state hydrogen atom is___.

Options:
A. $$
\mu\equiv-\frac{\partial( \Delta E )} {\partial B}=-\frac{e^{2} a^{2}} {4 8 m^2 c^{2}} B
$$
B. $$
\mu\equiv-\frac{\partial( \Delta E )} {\partial B}=-\frac{e^{4} a^{2}} {4 8 m c^{2}} B
$$
C. $$
\mu\equiv-\frac{\partial( \Delta E )} {\partial B}=-\frac{e^{2} a} {4 8 m c^{2}} B
$$
D. $$
\mu\equiv-\frac{\partial( \Delta E )} {\partial B}=\frac{e^{2} a^{2}} {4 8 m c^{2}} B
$$
E. $$
\mu\equiv-\frac{\partial( \Delta E )} {\partial B}=-\frac{2 e^{2} a^{2}} {4 8 m c^{2}} B
$$
F. $$
\mu\equiv-\frac{\partial( \Delta E )} {\partial B}=-\frac{e a^{2}} {16 m c^{2}} B
$$
G. $$
\mu\equiv-\frac{\partial( \Delta E )} {\partial B}=-\frac{e^{2} a^{2}} {4 m c^{2}} B
$$
H. $$
\mu\equiv-\frac{\partial( \Delta E )} {\partial B}=-\frac{e^{2} a^{2}} {4 8 m c^{2}} B
$$
I. $$
\mu\equiv-\frac{\partial( \Delta E )} {\partial B}=-\frac{e^{3} a^{2}} {4 8 m c^{2}} B
$$
J. $$
\mu\equiv-\frac{\partial( \Delta E )} {\partial B}=-\frac{e^{2} a^{3}} {4 8 m c^{3}} B
$$
Answer: H
The Doppler broadening of the spectral lines of atoms in the flame is____.

Options:
A. $$
4 0^{9} \, \mathrm{H z}
$$
B. $$
1 0^{8} \, \mathrm{H z}
$$
C. $$
1 0^{9} \, \mathrm{H z}
$$
D. $$
6 0^{9} \, \mathrm{H z}
$$
E. $$
7 0^{9} \, \mathrm{H z}
$$
F. $$
5 0^{8} \, \mathrm{H z}
$$
G. $$
8 0^{8} \, \mathrm{H z}
$$
H. $$
9 0^{8} \, \mathrm{H z}
$$
I. $$
2 0^{9} \, \mathrm{H z}
$$
J. $$
3 0^{9} \, \mathrm{H z}
$$
Answer: C
The dissociation energy of the $\mathrm{H_{2}}$ molecule is 4.46 eV, while the dissociation energy of the $\mathbf{D}_{2}$ molecule is 4.54 eV. Find the zero-point energy of the $\mathrm{H_{2}}$ molecule is_____.

Options:
A. $$
0. 2 4 ( \mathrm{e V} )
$$
B. $$
0. 3 1 ( \mathrm{e V} )
$$
C. $$
0. 2 5 ( \mathrm{e V} )
$$
D. $$
0. 2 8 ( \mathrm{e V} )
$$
E. $$
0. 2 6 ( \mathrm{e V} )
$$
F. $$
0. 3 3 ( \mathrm{e V} )
$$
G. $$
0. 2 9 ( \mathrm{e V} )
$$
H. $$
0. 3 2 ( \mathrm{e V} )
$$
I. $$
0. 2 7 ( \mathrm{e V} )
$$
J. $$
0. 3 0 ( \mathrm{e V} )
$$
Answer: I
The orbital angular momentum of the electron shell of a certain atom is $L=2$, and the spin quantum number is $S=0$; the angular momentum quantum number of the nucleus is $I={\frac{3}{2}}$. Therefore, the total angular momentum quantum number of this atom can be ____.

Options:
A. $$
\frac{8} {2}, \frac{5} {2}, \frac{3} {2}, \frac{1} {2}
$$
B. $$
\frac{6} {2}, \frac{5} {2}, \frac{3} {2}, \frac{1} {2}
$$
C. $$
\frac{7} {2}, \frac{5} {2}, \frac{3} {2}, \frac{1} {2}
$$
D. $$
\frac{7} {2}, \frac{5} {2}, \frac{2} {2}, \frac{1} {2}
$$
E. $$
\frac{7} {2}, \frac{4} {2}, \frac{3} {2}, \frac{1} {2}
$$
F. $$
\frac{9} {2}, \frac{5} {2}, \frac{3} {2}, \frac{1} {2}
$$
G. $$
\frac{7} {2}, \frac{5} {2}, \frac{3} {2}, \frac{2} {2}
$$
H. $$
\frac{7} {2}, \frac{5} {2}, \frac{5} {2}, \frac{1} {2}
$$
I. $$
\frac{7} {2}, \frac{6} {2}, \frac{3} {2}, \frac{1} {2}
$$
J. $$
\frac{7} {2}, \frac{5} {2}, \frac{3} {2}, \frac{3} {2}
$$
Answer: C
In a 100 MW reactor, the number of fissions per second is___.

Options:
A. $$
4 \times 1 0^{1 7}
$$
B. $$
2 \times 1 0^{1 8}
$$
C. $$
5 \times 1 0^{1 8}
$$
D. $$
9 . 5 \times 1 0^{1 7}
$$
E. $$
7 \times 1 0^{1 7}
$$
F. $$
3 . 5 \times 1 0^{1 8}
$$
G. $$
1 0^{1 8}
$$
H. $$
8 \times 1 0^{1 7}
$$
I. $$
6 \times 1 0^{1 8}
$$
J. $$
9 \times 1 0^{1 6}
$$
Answer: G
Assume the $^1\mathrm{H}^{35}\mathrm{Cl}$ molecule is approximated as a rigid dumbbell, with a nuclear distance of $1.29 \times 10^{-10} \mathrm{m}$. What is the frequency spacing of its far-infrared spectral lines? $( h = 6.6 \times 10^{-34} \mathrm{J} \cdot \mathrm{s}$ , one atomic mass unit $= 1.67 \times 10^{-27} \mathrm{kg}).$

Options:
A. $$
5. 8 \times1 0^{1 1} \mathrm{H z}
$$
B. $$
3. 6 \times1 0^{1 1} \mathrm{H z}
$$
C. $$
5. 5 \times1 0^{1 1} \mathrm{H z}
$$
D. $$
8. 1 \times1 0^{1 1} \mathrm{H z}
$$
E. $$
9. 5 \times1 0^{1 1} \mathrm{H z}
$$
F. $$
2. 3 \times1 0^{1 1} \mathrm{H z}
$$
G. $$
7. 8 \times1 0^{1 1} \mathrm{H z}
$$
H. $$
6. 2 \times1 0^{1 1} \mathrm{H z}
$$
I. $$
4. 9 \times1 0^{1 1} \mathrm{H z}
$$
J. $$
7. 0 \times1 0^{1 1} \mathrm{H z}
$$
Answer: H
Consider a system consisting of $N$ ($N \gg 1$) distinguishable, non-free-moving, non-interacting atoms. Each atom can occupy two non-degenerate energy levels, $0$ and $\varepsilon > 0$. $E / N$ is the average energy per atom.
In thermal equilibrium, based on $E / N$, what is the entropy per atom ( $S / N$ ) ?

Options:
A. $$
k \bigg[ \frac{E} {N \varepsilon} \mathrm{l n} \: \frac{1} {E}+\Big( 1-\frac{E} {N \varepsilon} \Big) \mathrm{l n} \: \frac{\varepsilon} {N} \bigg]
$$
B. $$
k \bigg[ \frac{\varepsilon} {N} \mathrm{l n} \: \frac{E} {N \varepsilon}+\Big( 1-\frac{E} {N \varepsilon} \Big)\mathrm{l n} \: \frac{N \varepsilon} {E} \bigg]
$$
C. $$
k \bigg[ \frac{E} {N \varepsilon} \mathrm{l n} \: \frac{N} {E}+\Big( 1-\frac{E} {N \varepsilon} \Big) \mathrm{l n} \: \varepsilon \bigg]
$$
D. $$
k \bigg[ \frac{N \varepsilon} {E} \mathrm{l n} \: \frac{E} {N \varepsilon}+\Big( 1+\frac{E} {N \varepsilon} \Big) \mathrm{l n} \: \frac{E} {N \varepsilon} \bigg]
$$
E. $$
k \bigg[ \frac{1}{N \varepsilon} \mathrm{l n} \: \frac{E} {N}+\Big( 1-\frac{E} {N \varepsilon} \Big) \mathrm{l n} \: \frac{1} {\varepsilon} \bigg]
$$
F. $$
k \bigg[ \frac{E} {N \varepsilon} \mathrm{l n} \: \frac{1} {\varepsilon}+\Big( 1+\frac{E} {N \varepsilon} \Big) \mathrm{l n} \: \frac{N \varepsilon} {E} \bigg]
$$
G. $$
k \bigg[ \frac{E} {N \varepsilon} \mathrm{l n} \: \varepsilon+\Big( 1-\frac{E} {N \varepsilon} \Big) \mathrm{l n} \: \frac{E} {N} \bigg]
$$
H. $$
k \bigg[ \frac{E} {N \varepsilon} \mathrm{l n} \: \frac{E} {N}+ \Big( 1-\frac{E} {N \varepsilon} \Big) \mathrm{l n} \: \frac{E} {N \varepsilon} \bigg]
$$
I. $$
k \bigg[ \frac{E} {N \varepsilon} \mathrm{l n} \: E+\Big( 1-\frac{E} {N \varepsilon} \Big) \mathrm{l n} \: \frac{1} {\varepsilon} \bigg]
$$
J. $$
k \bigg[ \frac{E} {N \varepsilon} \mathrm{l n} \: \frac{N \varepsilon} {E}+\Big( 1-\frac{E} {N \varepsilon} \Big) \mathrm{l n} \: \frac{1} {1-\frac{E} {N \varepsilon}} \bigg]
$$
Answer: J
$N$ spin-1/2 particles are arranged in a straight line, and interactions occur only between nearest neighbors. When both neighboring spins are either up or down, the interaction energy between them is $J$. When one neighboring spin is up and the other is down, the interaction energy is $-J$. (In the language of quantum mechanics, the interaction energy between neighbors $i$ and $j$ is $J \sigma_{2}^{i} \sigma_{2}^{j}$.) What is the partition function of this system at temperature $T$?

Options:
A. $$
2^{N} \mathrm{c o s h}^{N-1} \Big( \frac{J} {2 k T} \Big)
$$
B. $$
N^{2} \mathrm{c o s h}^{N-1} \Big( \frac{J} {k T} \Big)
$$
C. $$
2^{N} \mathrm{c o s}^{N-1} \Big( \frac{J} {k T} \Big)
$$
D. $$
2^{N} \mathrm{c o s h}^{N+1} \Big( \frac{J} {k T} \Big)
$$
E. $$
2^{N} \mathrm{e x p}^{N-1} \Big( \frac{J} {k T} \Big)
$$
F. $$
2^{N} \mathrm{c o s h}^{N-1} \Big( \frac{k T} {J} \Big)
$$
G. $$
2^{N} \mathrm{c o s h}^{N-1} \Big( \frac{J} {k T} \Big)
$$
H. $$
2^{N} \mathrm{s i n h}^{N-1} \Big( \frac{J} {k T} \Big)
$$
I. $$
2^{N} \mathrm{s i n}^{N-1} \Big( \frac{J} {k T} \Big)
$$
J. $$
2^{N} \mathrm{c o s h}^{2(N-1)} \Big( \frac{J} {k T} \Big)
$$
Answer: G