MikaStars39/nano-eval huggingface dataset:
A homogeneous circular ring is suspended horizontally. The lengths of the three suspension wires are all $l.$ When the ring is in equilibrium, the wires are vertical and attached to the ring at points $A, B, C,$ which divide the ring into three equal parts.What is the frequency of small-amplitude torsional vibrations of this ring ?

Options:
A. $\omega=\sqrt{\frac gl}$
B. $\omega=\frac{\sqrt{gl}}{2}$
C. $\omega=\sqrt{\frac {g}{l^2}}$
D. $\omega=\sqrt{\frac {g}{l^3}}$
E. $\omega=\frac {g}{\sqrt{l}}$
F. $\omega=\sqrt{\frac {5g}{4l}}$
G. $\omega=\frac{\sqrt {gl}}{3}$
H. $\omega=\sqrt{\frac {2g}{l}}$
I. $\omega=\sqrt{\frac {3g}{2l}}$
J. $\omega=\frac {g}{2 \sqrt{l}}$
Answer: A
The safety switch of the steam turbine is a pin A with a mass of $m = 0.225 \ \mathrm{kg}$, installed in a small hole at the front end of the turbine. The hole is drilled vertically into the shaft, and the pin is pressed into the hole by a spring. When the turbine rotates at a normal speed of $n = 1500 \, \mathrm{r} / \mathrm{min}$, the distance from the pin's center of gravity to the rotation axis is $l = 8.5 \; \mathrm{mm}$. When the turbine speed increases by 10%, the pin moves from its normal position due to the spring's force, reaching the position at $x = 4.5$ mm, where it hits one end of the lever $B$, causing the release of the movable hook. Consequently, the lever assembly connected to the hook closes the air valve of the turbine's safety mechanism. Assuming the spring force is proportional to the amount of compression.What is the stiffness coefficient of the spring ?

Options:
A. $$
c=8 9. 2 \mathrm{~ N / c m}.
$$
B. $$
c=5 2. 7 \mathrm{~ N / c m}.
$$
C. $$
c=7 8. 3 \mathrm{~ N / c m}.
$$
D. $$
c=8 3. 6 \mathrm{~ N / c m}.
$$
E. $$
c=9 5. 1 \mathrm{~ N / c m}.
$$
F. $$
c=6 5. 4 \mathrm{~ N / c m}.
$$
G. $$
c=7 6. 9 \mathrm{~ N / c m}.
$$
H. $$
c=9 2. 8 \mathrm{~ N / c m}.
$$
I. $$
c=1 0 1. 0 \mathrm{~ N / c m}.
$$
J. $$
c=8 0. 5 \mathrm{~ N / c m}.
$$
Answer: A
A mobile crane used for repairing street power grids is mounted on a vehicle with a mass of 1 ton. The crane's jib $K$ is installed on rod $L$, which can rotate around a horizontal axis $O$ perpendicular to the plane of the diagram. Initially, the crane is in a horizontal position and the vehicle is stationary. When the crane rotates by 60°.What is the displacement of the unbraked vehicle ?The homogeneous rod $L$ has a length of 3 meters and a mass of 100 kg, while the mass of the jib $K$ is 200 kg. The distance from the center of gravity $C$ to the axis $O$ is $OC = 3.5 \mathrm{~m}$. Ignore any resistance to motion.

Options:
A. Move 32.7 cm to the right.
B. Slide 17.3 cm backward.
C. Travel 32.7 cm to the front.
D. Move 25.4 cm to the right.
E. Travel 56.8 cm forward.
F. Drift 32.7 cm downward.
G. Shift 39.5 cm forward.
H. Move 32.7 cm to the left.
I. Move 48.2 cm to the left.
J. Shift 32.7 cm upward.
Answer: A
Calculate the heat released when 1 cm$^{3}$ of plutonium decays. It is known that the density of Pu$^{239}$ is 21 grams/cm$^{3}$, the half-life $T \!=\! 24,100$ years, and the energy of the emitted $\alpha$ particles is 2.3 million electron volts.

Options:
A. $$
8. 4 \cdot1 0^{-2} \text{cal/s}
$$
B. $$
9. 3 \cdot1 0^{-2} \text{cal/s}
$$
C. $$
3. 9 \cdot1 0^{-2} \text{cal/s}
$$
D. $$
9. 6 \cdot1 0^{-3} \text{cal/s}
$$
E. $$
8. 1 \cdot1 0^{-3} \text{cal/s}
$$
F. $$
8. 8 \cdot1 0^{-3} \text{cal/s}
$$
G. $$
4. 7 \cdot1 0^{-3} \text{cal/s}
$$
H. $$
9. 5 \cdot1 0^{-3} \text{cal/s}
$$
I. $$
9. 2 \cdot1 0^{-3} \text{cal/s}
$$
J. $$
8. 9 \cdot1 0^{-3} \text{cal/s}
$$
Answer: D
To measure the radioactivity of uranium ore, a Geiger-Müller counter instrument was used, calibrated from 0 to 500 counts per minute. With a normal background of 200 counts per minute, a sample containing a small amount of uranium was measured for 30 minutes. What is the statistically accurate value of this measurement?

Options:
A. ±27 pulses/day
B. ±23 pulses/day
C. ±30 pulses/minute
D. ±28 pulses/hour
E. ±26 pulses/minute
F. ±22 pulses/minute
G. ±25 pulses/minute
H. ±24 pulses/day
I. ±21 pulses/hour
J. ±19 pulses/hour
Answer: E
Measure the radioactivity of a C$^{14}$ sample using a counter tube filled with $\mathrm{CO_{2}}$. At this time, the partial pressure of $\mathrm{CO_{2}}$ is 48 mmHg, and the working volume of the counter tube is 50 cm$^{3}$. Try to calculate the specific radioactivity of $\mathrm{CH_{3}}$C$^{14}$OOH, expressed in pulses per minute per milligram. Assume the measured radioactivity is 1000 pulses per minute, and the counting efficiency is equal to 1.

Options:
A. 2.0×10 $^{3}$ pulses/min per millimole
B. 1.7×10 $^{4}$ pulses/min per millimole
C. 8.0×10 $^{3}$ pulses/min per milligram
D. 1.4×10 $^{4}$ pulses/min per milligram
E. 2.5×10 $^{4}$ pulses/min per millimole
F. 1.2×10 $^{4}$ pulses/min per millimole
G. 3.6×10 $^{4}$ pulses/min per millimole
H. 1.9×10 $^{4}$ pulses/min per milligram
I. 1.6×10 $^{4}$ pulses/min per milligram
J. 1.5×10 $^{3}$ pulses/min per millimole
Answer: I
From the uranium preparation enriched with $^{235}$U isotope and stored for one year, samples of $\mathrm{U X}_{2}$ and $\mathbf{U Y}_{\circ}$ were purified. The initial absolute $\beta$ radioactivity of the sample was 10 $^{5}$ particles/sec, which decreased to 10 $^{3}$ particles/sec after five days and nights. calculate the enrichment level of the$\mathrm{U^{286}}$ isotope in this sample.

Options:
A. 96.5%
B. 93.8%
C. 98.6%
D. 98.9%
E. 85.2%
F. 92.7%
G. 92.3%
H. 89.9%
I. 95.4%
J. 67.1%
Answer: A
From a sample of silk that has been stored for no less than one year, completely isolate $\mathbf{U} \mathbf{X}_{1}$ and purify it. Prepare solutions with equal volumes using the purified $U \mathbf{X_{1}}$ and a uranium sample that does not contain $U \mathbf{X_{1}}$, then measure their $\beta$ radioactivity under the same conditions. It was observed that the $\beta$ radioactivity decay curve for the $U \mathbf{X_{1}}$ sample intersects with the $\beta$ radioactivity growth curve of sample UI after 20 days. Try to determine the percentage loss of $\mathbf{U} \mathbf{X}_{1}$ during purification?

Options:
A. 28%
B. 15%
C. 22%
D. 18%
E. 25%
F. 20%
G. 30%
H. 27%
I. 24%
J. 17%
Answer: C
When neutrons bombard $C1^{37}$, $\gamma$ rays are emitted, and the residual nucleus is $\beta$-radioactive. After short-term neutron bombardment of a chlorine-containing target, its radioactivity is measured every ten minutes. After correcting for the background radiation, the readings are: 344, 267, 235, 189, 160, 145, 112, 97, 81, 65, 55, 50, 39, 37, 27, 25, 20, 14, 14, 11, 9. Determine the half-life of the $\beta$ radioactive source.

Options:
A. 37 minutes
B. 35 minutes
C. 32 minutes
D. 38 minutes
E. 39 minutes
F. 29 minutes
G. 33 minutes
H. 41 minutes
I. 30 minutes
Answer: E
In the electrolytic cell, there are 10 kilograms of mercury. To determine the percentage of mercury consumption in the cell, 0.1 grams of Hg $^{203}$ with a specific radioactivity of 0.1 millicurie/gram is added. After 1125 hours, 1 gram of mercury is taken as a sample. After correction for geometric factors and efficiency, its radioactivity is measured to be 1000 counts per minute. Calculate the percentage of mercury loss in the cell during this period.

Options:
A. 1.5%
B. 2%
C. 0.6%
D. 4%
E. 2.5%
F. 0.8%
G. 1%
H. 0.5%
I. 3%
J. 5%
Answer: G
When analyzing a mixture of boron isotopes, the neutron flux through the entire thin target is 10 $^{3}$ neutrons/second. Based on the flux intensity through the target, it is known that the efficiency of the neutron counter tube is 5%. The minimum detectable radioactivity is 100 pulses/minute. Calculate the sensitivity of using the neutron absorption method to analyze the content of boron-10. In the calculation, use the data of the effective cross-section of boron for thermal neutrons from the table, neglecting side reactions. Discuss the potential of using this method to determine the degree of separation of boron isotopes.

Options:
A. 0.68 grams
B. 0.73 milligrams
C. 0.74 decigrams
D. 0.75 milligrams
E. 0.71 centimeters
F. 0.72 nanograms
G. 0.77 kilograms
H. 0.69 picograms
I. 0.76 milliliters
J. 0.80 micrograms
Answer: B
In classic $\beta$ decay, what is the order of magnitude of the neutrino energy?
What is the relationship between the average lifetime of the 2P state spontaneous decay in hydrogen-like atoms such as $\mathrm{H, He^{+}, Li^{++}}$ and the atomic number $Z$?

Options:
A. $$
E_{v} {\approx} 2 \mathrm{M e V}.
$$
$$
\tau\propto A \propto Z^{-1}
$$
B. $$
E_{v} {\approx} 8 \mathrm{M e V}.
$$
$$
\tau\propto Z \propto A^{-4}
$$
C. $$
E_{v} {\approx} 10 \mathrm{M e V}.
$$
$$
\tau\propto A \propto Z^{-0.5}
$$
D. $$
E_{v} {\approx} 1 \mathrm{M e V}.
$$
$$
\tau\propto\frac{1} {A} \propto Z^{-4}
$$
E. $$
E_{v} {\approx} 5 \mathrm{M e V}.
$$
$$
\tau\propto Z^{-1} \propto A^{1}
$$
F. $$
E_{v} {\approx} 9 \mathrm{M e V}.
$$
$$
\tau\propto Z^{-2} \propto A^{2}
$$
G. $$
E_{v} {\approx} 3 \mathrm{M e V}.
$$
$$
\tau\propto A^{2} \propto Z^{-2}
$$
H. $$
E_{v} {\approx} 4 \mathrm{M e V}.
$$
$$
\tau\propto Z^{2} \propto A^{-2}
$$
I. $$
E_{v} {\approx} 6 \mathrm{M e V}.
$$
$$
\tau\propto Z^{-3} \propto A^{3}
$$
J. $$
E_{v} {\approx} 0.5 \mathrm{M e V}.
$$
$$
\tau\propto Z^{3} \propto A^{-3}
$$
Answer: D
Estimate the order of magnitude of the ratio of energy released by uranium fission to the energy released by the explosion of 1g of TNT is____.

Options:
A. $$ 9 \times 1 0^{5} $$
B. $$ 6 \times 1 0^{4} $$
C. $$ 3 \times 1 0^{7} $$
D. $$ 4 \times 1 0^{8} $$
E. $$ 1 \times 1 0^{6} $$
F. $$ 2 \times 1 0^{7} $$
G. $$
5 \times1 0^{6}
$$
H. $$ 7 \times 1 0^{5} $$
I. $$ 8 \times 1 0^{7} $$
J. $$ 3 \times 1 0^{6} $$
Answer: G
At a temperature of °C, the equilibrium vapor pressure of mercury $p=1.85 \times 10^{-4} \mathrm{mm Hg}$. If the vapor of mercury is quickly removed:
What is the numerical value of $r$ ?

Options:
A. $$
0. \, 6 5 \mathbf{k} \mathbf{g} \cdot\mathbf{s}^{-1} \cdot\mathbf{m}^{-2}
$$
B. $$
0. \, 8 5 \mathbf{k} \mathbf{g} \cdot\mathbf{s}^{-1} \cdot\mathbf{m}^{-2}
$$
C. $$
0. \, 7 0 \mathbf{k} \mathbf{g} \cdot\mathbf{s}^{-1} \cdot\mathbf{m}^{2}
$$
D. $$
0. \, 7 4 \mathbf{k} \mathbf{g} \cdot\mathbf{s}^{-1} \cdot\mathbf{m}^{-2}
$$
E. $$
1. \, 9 5 \mathbf{k} \cdot\mathbf{s}^{-1} \cdot\mathbf{m}^{-2}
$$
F. $$
0. \, 6 8 \mathbf{k} \mathbf{g} \cdot\mathbf{s}^{-1} \mathbf{m}^{-2}
$$
G. $$
1. \, 0 0 \mathbf{k}g \cdot\mathbf{s}^{-1} \cdot\mathbf{m}^{-2}
$$
H. $$
0. \, 9 2 \mathbf{k} \mathbf{g} \cdot\mathbf{s}^{-1} \cdot\mathbf{m}^{2}
$$
I. $$
1. \, 1 0 \mathbf{k} \mathbf{g} \cdot\mathbf{s}^{-1} \cdot\mathbf{m}^{-2}
$$
J. $$
0. \, 7 2 \mathbf{k} \mathbf{g} \cdot\mathbf{s}^{-1} \cdot\mathbf{m}^{-2}
$$
Answer: J
A cable with a double-layer dielectric insulation structure has capacitance and resistance for the first layer (inner layer) and second layer (outer layer) as follows: $C_{1} \!=\! 4000 \mathrm{pF}, \ R_{1} \!=\! 1500 \mathrm{M} \Omega; \ \ C_{2} \!=\! 3000 \mathrm{pF}, \ R_{2} \!=\! 1000 \mathrm{M} \Omega_{3}$. When a DC voltage of 50 kV is applied and $t=\infty$, what is the conduction current flowing through the insulation? How much charge is on $C_{1}$ and $C_{2}$ at this time?

Options:
A. $$
1 7~\mathrm{\mu A},\ 1.1\times10^{-4}\mathrm{C},\ 6.5\times10^{-5}\mathrm{C}
$$
B. $$
2 2~\mathrm{\mu A},\ 1.6\times10^{-4}\mathrm{C},\ 5.2\times10^{-5}\mathrm{C}
$$
C. $$
2 3~\mathrm{\mu A},\ 1.8\times10^{-4}\mathrm{C},\ 6.8\times10^{-5}\mathrm{C}
$$
D. $$
1 8~\mathrm{\mu A},\ 1.4\times10^{-4}\mathrm{C},\ 5.5\times10^{-5}\mathrm{C}
$$
E. $$
2 1~\mathrm{\mu A},\ 1.3\times10^{-4}\mathrm{C},\ 6.7\times10^{-5}\mathrm{C}
$$
F. $$
2 0~\mathrm{\mu A},\ 1.2\times10^{-4}\mathrm{C},\ 6\times10^{-5}\mathrm{C}
$$
G. $$
2 \times10^{1}~\mathrm{\mu A},\ 1.5\times10^{-4}\mathrm{C},\ 7\times10^{-5}\mathrm{C}
$$
H. $$
2 5~\mathrm{\mu A},\ 1.9\times10^{-4}\mathrm{C},\ 5.8\times10^{-5}\mathrm{C}
$$
I. $$
2 4~\mathrm{\mu A},\ 1.7\times10^{-4}\mathrm{C},\ 7.5\times10^{-5}\mathrm{C}
$$
J. $$
1 9~\mathrm{\mu A},\ 1.0\times10^{-4}\mathrm{C},\ 5\times10^{-5}\mathrm{C}
$$
Answer: F
Let $\mathrm{A=6460/cm, ~ B=1.9 \times 10^{5} ~ V/cm, ~ \gamma=0.025}$. What are the minimum breakdown voltage in the uniform electric field air gap and the minimum value of the product of pressure and gap distance?

Options:
A. $$ U_{\mathrm{b m i n}}=0. 3 0 0 0 \mathrm{k V} $$
B. $$ U_{\mathrm{b m i n}}=0. 3 0 5 5 \mathrm{k V} $$
C. $$ U_{\mathrm{b m i n}}=0. 2 9 3 5 \mathrm{k V} $$
D. $$ U_{\mathrm{b m i n}}=0. 3 1 5 0 \mathrm{k V} $$
E. $$
U_{\mathrm{b m i n}}=0. 2 9 4 5 \mathrm{k V}
$$
F. $$ U_{\mathrm{b m i n}}=0. 2 9 9 9 \mathrm{k V} $$
G. $$ U_{\mathrm{b m i n}}=0. 2 7 8 0 \mathrm{k V} $$
H. $$ U_{\mathrm{b m i n}}=0. 2 8 5 0 \mathrm{k V} $$
I. $$ U_{\mathrm{b m i n}}=0. 2 8 9 9 \mathrm{k V} $$
J. $$ U_{\mathrm{b m i n}}=0. 2 9 0 0 \mathrm{k V} $$
Answer: E
Given that the length of the cable is 100 meters, with the grounding lead at the cable's end sheath measuring 12 meters, $R_{1}= 5 \Omega,~L_{1}=126.35 \mu\mathrm{H},~L_{2}=M=120 \mu\mathrm{H},~L_{3}=20 \mu\mathrm{H},~L_{4} \to 0,~U_{3}=10 \mathrm{kV}$, and the motor's rated voltage is 6.3 kV, what is the lightning withstand capability of the motor when the cable section and FE work together?

Options:
A. $$60 \mathrm{kV}$$
B. $$55 \mathrm{kV}$$
C. $$65 \mathrm{kV}$$
D. $$50 \mathrm{kV}$$
E. $$90 \mathrm{kV}$$
F. $$85 \mathrm{kV}$$
G. $$80 \mathrm{kV}$$
H. $$95 \mathrm{kV}$$
I. $$70 \mathrm{kV}$$
J. $$75 \mathrm{kV}$$
Answer: D
The line voltage of a three-phase transformer is $U_{e}=110 \mathrm{kV}$, the capacity is $P = 31.5 \mathrm{MVA}$, and the core material is hot-rolled silicon steel sheet. The excitation current is $I\%=4\%$, with continuous windings, $\mathrm{C=3000 pF}$. What is the maximum overvoltage factor during no-load switching?

Options:
A. $$8.52$$
B. $$7.05$$
C. $$7.73$$
D. $$5.89$$
E. $$8.16$$
F. $$9.36$$
G. $$6.42$$
H. $$5.37$$
I. $$6.95$$
J. $$4.28$$
Answer: B
A 500kV power-frequency test transformer is expected not to experience corona discharge. How far at minimum should the high-voltage lead terminal's grading ring (radius 20cm) be from the wall?

Options:
A. $$47.8cm$$
B. $$62.3cm$$
C. $$45.7cm$$
D. $$51.9cm$$
E. $$59.6cm$$
F. $$57.9cm$$
G. $$50.4cm$$
H. $$78.1cm$$
I. $$66.5cm$$
J. $$53.3cm$$
Answer: D
The inner diameter of a smooth ceramic tube is 6 cm, with a wall thickness of $3 \text{ cm}$. If a guide rod with a diameter of 6 cm or 3 cm is installed inside the tube, what is the initial voltage for power frequency flashover discharge for each case (where the ceramic's $\varepsilon_{\mathrm{r}}=6$)?

Options:
A. $$
70. 00 k V,~1 0 0. 00 k V
$$
B. $$
60. 00 k V,~1 2 0. 00 k V
$$
C. $$
69. 00 k V,~1 0 8. 00 k V
$$
D. $$
65. 00 k V,~1 1 0. 00 k V
$$
E. $$
63. 00 k V,~1 1 9. 00 k V
$$
F. $$
68. 00 k V,~1 0 5. 00 k V
$$
G. $$
64. 12 k V,~1 1 8. 0 3 k V
$$
H. $$
55. 00 k V,~1 2 5. 00 k V
$$
I. $$
66. 00 k V,~1 1 5. 00 k V
$$
J. $$
61. 00 k V,~1 2 2. 00 k V
$$
Answer: G
If the gas pressure of $\mathrm{SF}_{6}$ gas-insulated electrical equipment is 0.75 MPa at 20°C, what is the gas density of $\mathrm{SF}_{6}$ in this equipment and what is the liquefaction temperature of $\mathrm{SF}_{6}$ gas in this equipment?

Options:
A. $$43.89,\ -18^{\circ}\mathrm{C}$$
B. $$55.12,\ -15^{\circ}\mathrm{C}$$
C. $$48.06,\ -25^{\circ}\mathrm{C}$$
D. $$50.14,\ -22^{\circ}\mathrm{C}$$
E. $$51.47,\ -23^{\circ}\mathrm{C}$$
F. $$46.23,\ -20^{\circ}\mathrm{C}
$$
G. $$47.25,\ -19^{\circ}\mathrm{C}$$
H. $$45.68,\ -21^{\circ}\mathrm{C}$$
I. $$42.37,\ -17^{\circ}\mathrm{C}$$
J. $$49.01,\ -12^{\circ}\mathrm{C}$$
Answer: F
A smooth ceramic rod with a radius of 5 cm has metal flanges at both the top and bottom. The insulation distance is 1 m. The volume resistivity $\rho_{\mathrm{v}}$ is $1 \times 10^{13} \, \Omega\cdot\mathrm{cm}$, while the surface resistivity $\rho_{\mathrm{s}}$ is $1 \times 10^{12} \, \Omega$. What are the measured insulation resistances with and without protective rings?

Options:
A. $$
6. 4 9 {\times} 1 0^{1 2}
$$
B. $$
5. 8 8 {\times} 1 0^{1 2}
$$
C. $$
3. 5 4 {\times} 1 0^{1 1}
$$
D. $$
1. 2 5 {\times} 1 0^{1 3}
$$
E. $$
9. 6 3 {\times} 1 0^{1 0}
$$
F. $$
2. 5 4 {\times} 1 0^{1 2}
$$
G. $$
4. 1 7 {\times} 1 0^{1 2}
$$
H. $$
7. 3 2 {\times} 1 0^{1 1}
$$
I. $$
4. 5 6 {\times} 1 0^{1 1}
$$
J. $$
8. 7 1 {\times} 1 0^{1 2}
$$
Answer: F
In the machining sequence, 1000 balls (each with a mass of 1g) are placed in a horizontal square trough with a side length of $L=2$ m and are given a translational kinetic energy of 100 J. The balls move in a chaotic manner. The collisions between the balls and between the balls and the walls of the container are elastic. What is the force they exert on the walls of the container?

Options:
A. 40N
B. 80N
C. 100N
D. 70N
E. 20N
F. 50N
G. 60N
H. 90N
I. 10N
J. 30N
Answer: F
There are two cylindrical tall containers each with a radius of $a$ and base at the same horizontal level. They are connected at the bottom by a slender tube with an inner diameter of $r$ and a length of $l$ (where $a \gg r$). The containers are filled with the same liquid having a density of $\rho$ and a viscosity of $\eta$. Initially, the liquid levels in the two containers are different, but the fluid flows slowly. How long does it take for the difference in liquid level between the two containers to reduce to half of its original value?

Options:
A. $$
\frac{4 a^{2} \eta\ l \mathrm{l n} \ 2} {r^{3} \rho g}
$$
B. $$
\frac{8 a^{2} \eta\ l \mathrm{l n} \ 2} {r^{4} \rho g}
$$
C. $$
\frac{4 a^{2} \eta\ l \mathrm{l n} \ 3} {r^{4} \rho g}
$$
D. $$
\frac{4 a^{2} \eta\ l \mathrm{l n} \ 2} {r^{4} \rho g}
$$
E. $$
\frac{4 a^{2} \eta\ r \mathrm{l n} \ 2} {r^{4} \rho g}
$$
F. $$
\frac{4 a^{3} \eta\ l \mathrm{l n} \ 2} {r^{4} \rho g}
$$
G. $$
\frac{2 a^{2} \eta\ l \mathrm{l n} \ 2} {r^{4} \rho g}
$$
H. $$
\frac{6 a^{2} \eta\ l \mathrm{l n} \ 2} {r^{4} \rho g}
$$
I. $$
\frac{4 a^{2} \eta\ l \mathrm{l n} \ 2} {r^{4} \rho}
$$
J. $$
\frac{4 a^{2} \eta\ l \mathrm{l n} \ 2} {r^{2} \rho g}
$$
Answer: D
In a highly rarefied gas with pressure $p$ and temperature $T$, there are two plates A and B moving parallel to each other at velocities $v_{\Lambda}$ and $v_{\mathrm{B}}$, respectively. what is the viscous force per unit area ?
( Assume the molar mass of the gas is $M$. )

Options:
A. $$
{\frac{2p} {3}} \cdot{\sqrt{\frac{M} {\pi R T}}} \cdot( 2v_{\mathrm{A}}-v_{\mathrm{B}} ) \,
$$
B. $$
{\frac{p} {3}} \cdot{\sqrt{\frac{2 M} {\pi R T}}} \cdot( v_{\mathrm{A}}+v_{\mathrm{B}} ) \,
$$
C. $$
{\frac{p} {4}} \cdot{\sqrt{\frac{3 M} {\pi R T}}} \cdot( v_{\mathrm{B}}-v_{\mathrm{A}} ) \,
$$
D. $$
{\frac{p} {\pi}} \cdot{\sqrt{\frac{2 M} { R T}}} \cdot( v_{\mathrm{A}}-v_{\mathrm{B}} ) \,
$$
E. $$
{\frac{p} {2}} \cdot{\sqrt{\frac{M} {2\pi R T}}} \cdot( v_{\mathrm{A}}-v_{\mathrm{B}} ) \,
$$
F. $$
{\frac{3p} {5}} \cdot{\sqrt{\frac{4 M} {\pi R T}}} \cdot( v_{\mathrm{B}}-v_{\mathrm{A}} ) \,
$$
G. $$
{\frac{p} {2}} \cdot{\sqrt{\frac{2 M} {\pi R T}}} \cdot( v_{\mathrm{A}}-v_{\mathrm{B}} ) \,
$$
H. $$
{p} \cdot{\sqrt{\frac{M} {\pi R T}}} \cdot( v_{\mathrm{A}}-v_{\mathrm{B}} ) \,
$$
I. $$
{\frac{p} {2}} \cdot{\sqrt{\frac{2 M} {\pi T}}} \cdot( v_{\mathrm{B}}-v_{\mathrm{A}} ) \,
$$
J. $$
{\frac{p} {2}} \cdot{\sqrt{\frac{M} {\pi R T}}} \cdot( v_{\mathrm{B}}-v_{\mathrm{A}} ) \,
$$
Answer: G
An ideal gas undergoes a Carnot cycle, producing a net work of 800 J when the heat source temperature is 100°C and the cooler temperature is 0°C. If the cooler temperature remains unchanged and the heat source temperature is increased to raise the net work to 1.60 $\times 10^{3}$ J, what is the efficiency of Carnot cycle at this time?
( Assume both cycles operate between the same two adiabatic lines. )

Options:
A. $$5 0. 2 \%$$
B. $$3 6. 8 \%$$
C. $$4 9. 3 \%$$
D. $$
4 2. 3 \%
$$
E. $$5 1. 8 \%$$
F. $$4 8. 9 \%$$
G. $$4 0. 7 \%$$
H. $$4 5. 1 \%$$
I. $$3 9. 5 \%$$
J. $$3 7. 6 \%$$
Answer: D
A copper container with a mass of $m_{1}=200 \mathrm{g}$ and a specific heat capacity of $c_{1}=388 \mathrm{J/(kg} \cdot \mathrm{K})$ has two tubes that are open to the outside, with the rest of the container being sealed. First, some ice is placed in the container. After reaching thermal equilibrium, the water that has melted is poured out, leaving $m_{2}=20 \mathrm{g}$ of ice remaining in the container. Then, water vapor at 100°C is introduced through one tube while the other tube remains open. After the steam inside the container mixes and contacts the ice, it escapes through the open tube. The escaping steam is still at 100°C. After some time, due to the effect of the steam, the ice in the container fully melts, turning into water at $t=40 \degree \mathrm{C}$. How many grams of water are there in total in the container?

Options:
A. $$32.0g$$
B. $$18.5g$$
C. $$27.3g$$
D. $$15.0g$$
E. $$22.7g$$
F. $$20.0g$$
G. $$23.6g$$
H. $$25.2g$$
I. $$28.5g$$
J. $$30.2g$$
Answer: H
In a $\mathbf{U}$-shaped capillary tube, one tube has a radius of $r_{1}=1 \times 10^{-3} \mathrm{~m}$, and the other tube has a radius of $r_{2}=2 \times 10^{-3} \mathrm{~m}$. After filling the capillary tubes with some mercury, one tube is connected to a vacuum pump. What should be the difference in air pressure for the mercury surfaces in the two tubes to reach the same height?
( The surface tension coefficient of mercury is $\sigma=0.49 \mathrm{~N/m}$. )

Options:
A. $$
\approx1 7 5 4 \ \mathrm{P a}
$$
B. $$
\approx1 5 4 7 \ \mathrm{P a}
$$
C. $$
\approx1 6 0 2 \ \mathrm{P a}
$$
D. $$
\approx1 2 5 0 \ \mathrm{P a}
$$
E. $$
\approx1 4 6 6 \ \mathrm{P a}
$$
F. $$
\approx1 8 2 5 \ \mathrm{P a}
$$
G. $$
\approx1 3 5 9 \ \mathrm{P a}
$$
H. $$
\approx1 9 0 3 \ \mathrm{P a}
$$
I. $$
\approx1 8 9 8 \ \mathrm{P a}
$$
J. $$
\approx1 3 2 0 \ \mathrm{P a}
$$
Answer: E
A horizontal string with a mass of 0.05 kg is fixed at one end, while a 0.2 kg mass block is suspended on the other end through a pulley. Determine the wave speed of the transverse wave in the string; the fundamental frequency and the first overtone frequency of the string's transverse vibration; if only the first overtone is present in the string's vibration, what is the ratio of the displacement amplitude at the antinode to the amplitude at the location of the suspended mass block?

Options:
A. 7.32 m/s; 0.56 Hz, 2.5 Hz; approximately 12
B. 6.55 m/s; 0.45 Hz, 3.8 Hz; approximately 11
C. 5.89 m/s; 0.62 Hz, 3.5 Hz; approximately 15
D. 5.78 m/s; 0.48 Hz, 3.3 Hz; approximately 16
E. 6.26 m/s; 0.48 Hz, 3.2 Hz; approximately 13
F. 6.26 m/s; 0.52 Hz, 3.0 Hz; approximately 12
G. 7.01 m/s; 0.48 Hz, 3.1 Hz; approximately 14
H. 6.10 m/s; 0.50 Hz, 2.9 Hz; approximately 10
I. 6.26 m/s; 0.49 Hz, 3.4 Hz; approximately 14
J. 6.40 m/s; 0.47 Hz, 2.7 Hz; approximately 15
Answer: E
A 20 cm long annealed steel rod clamped at one end has a square cross-section with a side length of 1 cm. What are the four lowest transverse vibration frequencies? How would the frequencies change if the cross-section were circular with a radius of 0.5 cm? If the cross-section is a rectangle with one side of length $a$ and the other side of length $2a$, what value must $a$ be for the rod's lowest frequency to be 250 Hz? (For steel, $\rho = 7700 \ \mathrm{kg/m}^{3}$, $E = 2 \times 10^{11} \ \mathrm{N/m}^{2}$)

Options:
A. 208 Hz,1275 Hz,3590 Hz,7045 Hz;183 Hz;1113 Hz,3135 Hz,6150 Hz; $a \,=\, 0. 5 9$ cm
B. 203 Hz,1292 Hz,3645 Hz,7085 Hz;177 Hz;1110 Hz,3145 Hz,6160 Hz; $a \,=\, 0. 6 6$ cm
C. 200 Hz,1295 Hz,3650 Hz,7065 Hz;175 Hz;1108 Hz,3140 Hz,6110 Hz; $a \,=\, 0. 6 3$ cm
D. 215 Hz,1280 Hz,3620 Hz,7080 Hz;182 Hz;1115 Hz,3120 Hz,6125 Hz; $a \,=\, 0. 5 8$ cm
E. 209 Hz,1310 Hz,3625 Hz,7035 Hz;174 Hz;1125 Hz,3115 Hz,6100 Hz; $a \,=\, 0. 5 7$ cm
F. 204 Hz,1285 Hz,3605 Hz,7060 Hz;176 Hz;1105 Hz,3150 Hz,6115 Hz; $a \,=\, 0. 6 4$ cm
G. 205 Hz,1290 Hz,3610 Hz,7075 Hz;178 Hz;1118 Hz,3129 Hz,6133 Hz; $a \,=\, 0. 6 1$ cm
H. 210 Hz,1300 Hz,3600 Hz,7050 Hz;180 Hz;1120 Hz,3130 Hz,6140 Hz; $a \,=\, 0. 6 5$ cm
I. 206 Hz,1270 Hz,3585 Hz,7055 Hz;179 Hz;1117 Hz,3110 Hz,6135 Hz; $a \,=\, 0. 6 0$ cm
J. 207 Hz,1305 Hz,3615 Hz,7090 Hz;181 Hz;1122 Hz,3125 Hz,6105 Hz; $a \,=\, 0. 6 2$ cm
Answer: G
The diaphragm of a capacitive microphone is a circular aluminum membrane fixed around its perimeter, with a diameter of $0.03 \, \mathrm{m}$ and a thickness of $2.0 \times 10^{-5} \, \mathrm{m}$. It is known that the maximum tensile stress aluminum can withstand is $2.0 \times 10^{8} \, \mathrm{Pa}$. Please calculate: What is the maximum possible tension that can be reached in the aluminum membrane? What is the fundamental frequency of the membrane at this tension? If the membrane surface is subjected to a sound pressure with a frequency of 500 Hz and an amplitude of 2.0 Pa, what is the displacement amplitude at the center of the membrane? Under the above conditions, what is the average displacement amplitude of the membrane?

Options:
A. 4000 N/m;6.95 kHz;$2.8\times10^{-8}$;$1.2\times10^{-8}$m
B. 4500 N/m;7.20 kHz;$2.0\times10^{-8}$;$1.0\times10^{-8}$m
C. 3800 N/m;5.75 kHz;$3.2\times10^{-8}$;$1.4\times10^{-8}$m
D. 5000 N/m;8.00 kHz;$3.0\times10^{-8}$;$2.0\times10^{-8}$m
E. 4200 N/m;7.00 kHz;$2.6\times10^{-8}$;$1.1\times10^{-8}$m
F. 3300 N/m;6.20 kHz;$2.7\times10^{-8}$;$1.0\times10^{-8}$m
G. 5200 N/m;7.80 kHz;$3.3\times10^{-8}$;$1.8\times10^{-8}$m
H. 3000 N/m;6.50 kHz;$2.9\times10^{-8}$;$1.3\times10^{-8}$m
I. 4800 N/m;7.50 kHz;$2.4\times10^{-8}$;$1.6\times10^{-8}$m
J. 3500 N/m;5.50 kHz;$3.5\times10^{-8}$;$1.5\times10^{-8}$m
Answer: A
In air at 20°C, what are the particle displacement amplitude, particle velocity amplitude, sound pressure amplitude, and average sound energy density of a plane sound wave with a frequency of 1000 Hz and a sound pressure level of 0 dB? If the sound pressure level is 120 dB, what are the values of these quantities? What sound pressure level is needed for the air particle velocity to reach the same value as the speed of sound? (Reference value is $2 \times 10^{-5}$ Pa)

Options:
A. $\mathrm{ 1. 0 3 \times1 0^{-8} ~ m, 6. 2 \times1 0^{-5} ~ m / s, 2. 3 \times1 0^{-5} ~ P a, 2. 3 \times1 0^{-1 5} ~ J/ m^{3} ~ ; 1. 0 3 \times1 0^{-5} ~ m ; 0. 0 7 5 ~ m / s ~ m^{3} ~.}2.2 \times1 0^{-3} ~ J /m^{3}$; 204 Pa (linear acoustic failure).
B. $\mathrm{ 1. 0 9 \times1 0^{-8} ~ m, 6. 5 \times1 0^{-5} ~ m / s, 2. 6 \times1 0^{-5} ~ P a, 2. 6 \times1 0^{-1 5} ~ J/ m^{3} ~ ; 1. 0 9 \times1 0^{-5} ~ m ; 0. 0 7 1 ~ m / s ~ m^{3} ~.}2.5 \times1 0^{-3} ~ J /m^{3}$; 200 Pa (linear acoustic failure).
C. $\mathrm{ 1. 0 4 \times1 0^{-8} ~ m, 6. 3 \times1 0^{-5} ~ m / s, 2. 4 \times1 0^{-5} ~ P a, 2. 4 \times1 0^{-1 5} ~ J/ m^{3} ~ ; 1. 0 4 \times1 0^{-5} ~ m ; 0. 0 7 4 ~ m / s ~ m^{3} ~.}2.3 \times1 0^{-3} ~ J /m^{3}$; 203 Pa (linear acoustic failure).
D. $\mathrm{ 1. 0 5 \times1 0^{-8} ~ m, 6. 4 \times1 0^{-5} ~ m / s, 2. 5 \times1 0^{-5} ~ P a, 2. 5 \times1 0^{-1 5} ~ J/ m^{3} ~ ; 1. 0 5 \times1 0^{-5} ~ m ; 0. 0 7 2 ~ m / s ~ m^{3} ~.}2.4 \times1 0^{-3} ~ J /m^{3}$; 201 Pa (linear acoustic failure).
E. $\mathrm{ 1. 1 1 \times1 0^{-8} ~ m, 7. 0 \times1 0^{-5} ~ m / s, 3. 1 \times1 0^{-5} ~ P a, 3. 1 \times1 0^{-1 5} ~ J/ m^{3} ~ ; 1. 1 1 \times1 0^{-5} ~ m ; 0. 0 7 3 ~ m / s ~ m^{3} ~.}3.0 \times1 0^{-3} ~ J /m^{3}$; 202 Pa (linear acoustic failure).
F. $\mathrm{ 1. 0 7 \times1 0^{-8} ~ m, 6. 7 \times1 0^{-5} ~ m / s, 2. 8 \times1 0^{-5} ~ P a, 2. 8 \times1 0^{-1 5} ~ J/ m^{3} ~ ; 1. 0 7 \times1 0^{-5} ~ m ; 0. 0 6 8 ~ m / s ~ m^{3} ~.}2.7 \times1 0^{-3} ~ J /m^{3}$; 197 Pa (linear acoustic failure).
G. $\mathrm{ 1. 1 0 \times1 0^{-8} ~ m, 6. 9 \times1 0^{-5} ~ m / s, 3. 0 \times1 0^{-5} ~ P a, 3. 0 \times1 0^{-1 5} ~ J/ m^{3} ~ ; 1. 1 0 \times1 0^{-5} ~ m ; 0. 0 7 0 ~ m / s ~ m^{3} ~.}2.9 \times1 0^{-3} ~ J /m^{3}$; 199 Pa (linear acoustic failure).
H. $\mathrm{ 1. 0 6 \times1 0^{-8} ~ m, 6. 6 \times1 0^{-5} ~ m / s, 2. 7 \times1 0^{-5} ~ P a, 2. 7 \times1 0^{-1 5} ~ J/ m^{3} ~ ; 1. 0 6 \times1 0^{-5} ~ m ; 0. 0 6 7 ~ m / s ~ m^{3} ~.}2.6 \times1 0^{-3} ~ J /m^{3}$; 196 Pa (linear acoustic failure).
I. $\mathrm{ 1. 2 0 \times1 0^{-8} ~ m, 7. 1 \times1 0^{-5} ~ m / s, 3. 2 \times1 0^{-5} ~ P a, 3. 2 \times1 0^{-1 5} ~ J/ m^{3} ~ ; 1. 2 0 \times1 0^{-5} ~ m ; 0. 0 7 6 ~ m / s ~ m^{3} ~.}3.1 \times1 0^{-3} ~ J /m^{3}$; 205 Pa (linear acoustic failure).
J. $\mathrm{ 1. 0 8 \times1 0^{-8} ~ m, 6. 8 \times1 0^{-5} ~ m / s, 2. 9 \times1 0^{-5} ~ P a, 2. 9 \times1 0^{-1 5} ~ J/ m^{3} ~ ; 1. 0 8 \times1 0^{-5} ~ m ; 0. 0 6 9 ~ m / s ~ m^{3} ~.}2.8 \times1 0^{-3} ~ J /m^{3}$; 198 Pa (linear acoustic failure).
Answer: F
Given that the density of the solution is $800 \, \mathrm{kg/m}^{3}$, and the speed of sound is $1300 \, \mathrm{m/s}$, try to determine: the critical angle of incidence for a plane wave entering water from this solution; if the angle of incidence in the solution is $40^\circ$, what is the transmission coefficient of sound power into the water?

Options:
A. $$
6 4. 0^{\circ} ; 0. 8 0
$$
B. $$
6 2. 2^{\circ} ; 0. 8 5
$$
C. $$
6 1. 4^{\circ} ; 0. 9 5
$$
D. $$
6 4. 5^{\circ} ; 0. 9 8
$$
E. $$
5 9. 7^{\circ} ; 0. 7 0
$$
F. $$
6 3. 0^{\circ} ; 0. 8 2
$$
G. $$
7 0. 0^{\circ} ; 0. 8 9
$$
H. $$
6 6. 1^{\circ} ; 0. 7 5
$$
I. $$
6 0. 9^{\circ} ; 0. 9 2
$$
J. $$
5 8. 3^{\circ} ; 0. 9 3
$$
Answer: C
A plane sound wave of 200 Hz in the air is incident perpendicularly on a sound-absorbing wall with a normal acoustic impedance of $(1000-\mathrm{j} \, 2000) \, \mathrm{Rayl}$. Determine: What is the standing wave ratio? The positions of the first two nodes?

Options:
A. 14.5; 0.35 m,1.18.
B. 13.7; 0.33 m,1.21.
C. 11.9; 0.36 m,1.28.
D. 12.3; 0.38 m,1.24.
E. 14.0; 0.32 m,1.25.
F. 12.0; 0.37 m,1.26.
G. 10.8; 0.42 m,1.20.
H. 11.5; 0.39 m,1.30.
I. 11.2; 0.40 m,1.19.
J. 13.2; 0.34 m,1.22.
Answer: D
A pulsating spherical source with a radius of 0.01 m emits spherical waves at 14 kHz into water. If it is placed at the center of a spherical sealed container filled with oil, with a container radius of 6 cm, whose shell is very thin and the effect on sound wave penetration can be neglected, and then placed in open water. Now, if a sound pressure value of 10 dyne/cm$^{2}$ is to be obtained at a distance of 1 km from the center of the sphere, what is the radiated acoustic power of the emitter? What is the amplitude of the vibrational velocity at the surface of the spherical source? (The density and sound speed of the oil are 0.8 g/cm$^{3}$ and 1400 m/s, respectively.)

Options:
A. $$
5. 3 0 \ \mathrm{w}, 0. 1 8 \ \mathrm{m / s }.
$$
B. $$
5. 1 4 \ \mathrm{w}, 0. 2 0 \ \mathrm{m / s }.
$$
C. $$
6. 0 0 \ \mathrm{w}, 0. 1 7 \ \mathrm{m / s }.
$$
D. $$
5. 0 5 \ \mathrm{w}, 0. 2 3 \ \mathrm{m / s }.
$$
E. $$
4. 8 9 \ \mathrm{w}, 0. 2 1 \ \mathrm{m / s }.
$$
F. $$
6. 1 2 \ \mathrm{w}, 0. 1 6 \ \mathrm{m / s }.
$$
G. $$
5. 1 0 \ \mathrm{w}, 0. 1 9 \ \mathrm{m / s }.
$$
H. $$
4. 9 0 \ \mathrm{w}, 0. 1 5 \ \mathrm{m / s }.
$$
I. $$
5. 2 2 \ \mathrm{w}, 0. 2 2 \ \mathrm{m / s }.
$$
J. $$
5. 1 4 \ \mathrm{w}, 0. 1 7 \ \mathrm{m / s }.
$$
Answer: J
A circular piston sound source with a diameter of 30 cm radiates sound waves into an infinite water domain, operating at a frequency of 10 kHz with a sound power of 1000 W. Directly 1 km in front of this sound source, there is a rigid sphere with a diameter of 1 cm. Determine the intensity of the sound waves scattered back by this rigid sphere.

Options:
A. 9.85·10 $^{-3}$W/m$^{2}$
B. 2.20·10 $^{-3}$W/m$^{2}$
C. 6.17·10 $^{-3}$W/m$^{2}$
D. 5.00·10 $^{-3}$W/m$^{2}$
E. 4.05·10 $^{-4}$W/m$^{2}$
F. 8.95·10 $^{-3}$W/m$^{2}$
G. 1.50·10 $^{-2}$W/m$^{2}$
H. 7.30·10 $^{-3}$W/m$^{2}$
I. 5.54·10 $^{-3}$W/m$^{2}$
J. 3.06·10 $^{-3}$W/m$^{2}$
Answer: J
A limitless exponential horn radiates 1 $\mathbf{w}$ of sound power at a frequency of 250 Hz. The horn's throat radius is $0.03 \, \mathrm{m}$, and the flare constant is $m = 5$. What is the cutoff frequency of the horn? To produce 1 $\mathbf{w}$ of sound power output, what is the amplitude of the throat's volume velocity? If the diaphragm radius of the drive unit connected to the horn is 0.05 m, what is its peak displacement amplitude to produce the aforementioned volume velocity?

Options:
A. 148 Hz;3.9 × 10 $^{-3}$m $^{3}$/s;3.5 × 10 $^{-4}$m
B. 125 Hz;4.0 × 10 $^{-3}$m $^{3}$/s;2.9 × 10 $^{-4}$m
C. 136 Hz;4.0 × 10 $^{-3}$m $^{3}$/s;3.2 × 10 $^{-4}$m
D. 142 Hz;3.8 × 10 $^{-3}$m $^{3}$/s;3.6 × 10 $^{-4}$m
E. 140 Hz;4.4 × 10 $^{-3}$m $^{3}$/s;3.3 × 10 $^{-4}$m
F. 155 Hz;4.3 × 10 $^{-3}$m $^{3}$/s;3.4 × 10 $^{-4}$m
G. 124 Hz;4.5 × 10 $^{-3}$m $^{3}$/s;3.0 × 10 $^{-4}$m
H. 131 Hz;3.7 × 10 $^{-3}$m $^{3}$/s;3.7 × 10 $^{-4}$m
I. 134 Hz;4.2 × 10 $^{-3}$m $^{3}$/s;3.1 × 10 $^{-4}$m
J. 160 Hz;4.1 × 10 $^{-3}$m $^{3}$/s;2.8 × 10 $^{-4}$m
Answer: C
A loudspeaker operates within an infinitely large baffle and is assumed to radiate into half space, with an available power efficiency of 5%. At a distance of 6 meters from the loudspeaker, there is a dynamic microphone, with an open-circuit receiving voltage sensitivity of -90 dB (reference value $\mathrm{1/\mu bar}$). Assuming the loudspeaker radiates a spherical wave, and the microphone's output impedance is primarily resistive, with a value of 30Ω. If the loudspeaker's available power is 10W, what is the power in the 30Ω resistor connected to the microphone?

Options:
A. 7.8×10 $^{-8}$W
B. 5.7×10 $^{-9}$W
C. 9.4×10 $^{-9}$W
D. 8.9×10 $^{-6}$W
E. 3.5×10 $^{-8}$W
F. 6.1×10 $^{-10}$W
G. 1.0×10 $^{-7}$W
H. 1.7×10 $^{-9}$W
I. 2.3×10 $^{-9}$W
J. 4.2×10 $^{-7}$W
Answer: H
Determine the loudness level and loudness of a 200 Hz pure tone with a sound intensity level of 50 dB. How many decibels does the sound intensity level need to increase by in order for the loudness of this pure tone to double?

Options:
A. 52 phon,2.0 sone;6 dB
B. 48 phon,2.5 sone;8 dB
C. 51 phon,2.3 sone;11 dB
D. 47 phon,2.4 sone;7 dB
E. 50 phon,2.1 sone;9 dB
F. 46 phon,2.6 sone;10 dB
G. 53 phon,2.2 sone;12 dB
H. 49 phon,1.9 sone;10 dB
I. 55 phon,1.8 sone;7 dB
J. 54 phon,1.7 sone;13 dB
Answer: E
10.00 grams of impure D-glucose are dissolved in distilled water and diluted to $100ml$. Using a $2dm$ polarimeter sample tube, first fill the tube with distilled water and record the zero reading as +2.020°. Then fill the tube with the test solution and observe the result at 20°C. The reading is +5.750°. Calculate the percentage content of the D-glucose. (D-glucose $[\alpha]^{20}_{D}=+52.5^{\circ}$)

Options:
A. $$71\%$$
B. $$95\%$$
C. $$78\%$$
D. $$64\%$$
E. $$67\%$$
F. $$89\%$$
G. $$56\%$$
H. $$85\%$$
I. $$42\%$$
J. $$38\%$$
Answer: A
An incident nucleon collides with another stationary nucleon to produce a $\pi$ meson, with the reaction given by
$$
\mathrm{N+N \to N+N+\pi}
$$
What is the threshold kinetic energy $T_{0}$ for this reaction ?

Options:
A. $$
{\frac{1} {2 m_{\mathrm{N}}}} ( 5 m_{\mathrm{N}}+m_{\pi} ) m_{\pi} c^{2}
$$
B. $$
{\frac{1} {2 m_{\mathrm{N}}}} ( 5 m_{\mathrm{N}}-m_{\pi} ) m_{\pi} c^{2}
$$
C. $$
{\frac{1} {3 m_{\mathrm{N}}}} ( 4 m_{\mathrm{N}}-2 m_{\pi} ) m_{\pi} c^{2}
$$
D. $$
{\frac{1} {2 m_{\mathrm{N}}}} ( 4 m_{\mathrm{N}}+m_{\pi} ) m_{\pi} c^{2}
$$
E. $$
{\frac{1} {2 m_{\mathrm{N}}}} ( 2 m_{\mathrm{N}}+3 m_{\pi} ) m_{\pi} c^{2}
$$
F. $$
{\frac{1} {5 m_{\mathrm{N}}}} ( 6 m_{\mathrm{N}}-m_{\pi} ) m_{\pi} c^{2}
$$
G. $$
{\frac{1} {2 m_{\mathrm{N}}}} ( 3 m_{\mathrm{N}}+m_{\pi} ) m_{\pi} c^{2}
$$
H. $$
{\frac{1} {2 m_{\mathrm{N}}}} ( 4 m_{\mathrm{N}}+2 m_{\pi} ) m_{\pi} c^{2}
$$
I. $$
{\frac{1} {4 m_{\mathrm{N}}}} ( 3 m_{\mathrm{N}}+2 m_{\pi} ) m_{\pi} c^{2}
$$
J. $$
{\frac{1} {3 m_{\mathrm{N}}}} ( 2 m_{\mathrm{N}}+m_{\pi} ) m_{\pi} c^{2}
$$
Answer: D
In the $\mathrm{p+p \to\ p \pi^{+}+d}$ reaction, high-energy protons from an accelerator hit a stationary proton, producing $\pi^{+}$ and a deuteron. Calculate the kinetic energy $T$ of the incident proton in the laboratory frame, given that the masses of the particles are $m_{\mathrm{p}}=938 \, \mathrm{MeV}/c^{2}$, $m_{\mathrm{d}}=1874 \, \mathrm{MeV}/c^{2}$, and $m_{\pi}=140 \, \mathrm{MeV}/c^{2}$.

Options:
A. $$
\approx2 7 6. 6 ( \mathrm{M e V} )
$$
B. $$
\approx2 9 8. 3 ( \mathrm{M e V} )
$$
C. $$
\approx2 6 8. 4 ( \mathrm{M e V} )
$$
D. $$
\approx2 9 3. 5 ( \mathrm{M e V} )
$$
E. $$
\approx2 6 2. 1 ( \mathrm{M e V} )
$$
F. $$
\approx3 0 4. 4 ( \mathrm{M e V} )
$$
G. $$
\approx3 1 0. 2 ( \mathrm{M e V} )
$$
H. $$
\approx2 7 2. 9 ( \mathrm{M e V} )
$$
I. $$
\approx2 8 6. 1 ( \mathrm{M e V} )
$$
J. $$
\approx2 5 0. 7 ( \mathrm{M e V} )
$$
Answer: I
A neutron with a rest mass of $940 \mathrm{MeV}$ and a half-life of 13 minutes is 5,000 light-years away from Earth. How much energy is required for this neutron to reach the earth at the end of its first half-life?

Options:
A. $$
8. 2 \times1 0^{1 1} \mathrm{M e V}
$$
B. $$
2. 4 \times1 0^{1 1} \mathrm{M e V}
$$
C. $$
5. 4 \times1 0^{1 1} \mathrm{M e V}
$$
D. $$
3. 6 \times1 0^{1 1} \mathrm{M e V}
$$
E. $$
2. 3 \times1 0^{1 1} \mathrm{M e V}
$$
F. $$
6. 5 \times1 0^{1 1} \mathrm{M e V}
$$
G. $$
1. 9 \times1 0^{1 1} \mathrm{M e V}
$$
H. $$
4. 7 \times1 0^{1 1} \mathrm{M e V}
$$
I. $$
1. 8 \times1 0^{1 1} \mathrm{M e V}
$$
J. $$
7. 1 \times1 0^{1 1} \mathrm{M e V}
$$
Answer: G
The rest average lifetime of a charged $\pi$ meson is $2.6 \times 10^{-8} \mathrm{s}$. After a monoenergetic beam of $\pi$ mesons produced by an accelerator travels a distance of 10m, $10\%$ of the $\pi$ mesons have decayed. What are the momentum and kinetic energy of the $\pi$ mesons ?

Options:
A. $$
1. 7 1 ( \mathrm{G e V} / c )
$$
$$
\approx1. 5 8 \mathrm{G e V}
$$
B. $$
0. 8 8 ( \mathrm{G e V} / c )
$$
$$
\approx3. 8 4 \mathrm{G e V}
$$
C. $$
5. 9 5 ( \mathrm{G e V} / c )
$$
$$
\approx2. 1 9 \mathrm{G e V}
$$
D. $$
2. 1 3 ( \mathrm{G e V} / c )
$$
$$
\approx2. 6 5 \mathrm{G e V}
$$
E. $$
0. 5 7 ( \mathrm{G e V} / c )
$$
$$
\approx3. 0 2 \mathrm{G e V}
$$
F. $$
4. 2 8 ( \mathrm{G e V} / c )
$$
$$
\approx1. 9 3 \mathrm{G e V}
$$
G. $$
3. 0 9 ( \mathrm{G e V} / c )
$$
$$
\approx0. 9 7 \mathrm{G e V}
$$
H. $$
2. 4 9 ( \mathrm{G e V} / c )
$$
$$
\approx5. 2 8 \mathrm{G e V}
$$
I. $$
1. 3 4 ( \mathrm{G e V} / c )
$$
$$
\approx4. 7 5 \mathrm{G e V}
$$
J. $$
3. 6 7 ( \mathrm{G e V} / c )
$$
$$
\approx0. 5 9 \mathrm{G e V}
$$
Answer: A
A water pipe with a radius of $r_{\mathrm{o}}=150 \mathrm{mm}$ is tested at a water temperature of $t=15 \mathrm{^{\circ}C}$, yielding data with a cross-sectional average flow velocity of $v = 3.0 \mathrm{m/s}$ and a head loss coefficient along the path of $\lambda=0.015$. If the time-averaged velocity gradient at the point $r=0.5 r_{0}$ is 4.34/s, find the turbulent additional shear stress at this point.

Options:
A. $$
9.447(Pa)
$$
B. $$
8.433(Pa)
$$
C. $$
7.892(Pa)
$$
D. $$
5.876(Pa)
$$
E. $$
6.998(Pa)
$$
F. $$
7.321(Pa)
$$
G. $$
8.112(Pa)
$$
H. $$
9.132(Pa)
$$
I. $$
7.605(Pa)
$$
J. $$
8.256(Pa)
$$
Answer: B
A certain highway requires embankment with a specific dry density of $\boldsymbol{\gamma}_{\mathrm{d}}=17.8 \mathbf{kN} / \mathbf{m}^{3}$, and the required volume for fill is 400,000 $\mathbf{m}^{3}$. The survey results for a particular material site are as follows: soil particle specific gravity $G_{N}=2.7$, moisture content $w=15.2\%$, and void ratio $e=0.823$. Which of the following options (in 10,000 $\mathbf{m}^{3}$) is the minimum required reserve at this material site to meet the demand?

Options:
A. 88
B. 110
C. 102
D. 92
E. 113
F. 104
G. 96
H. 85
I. 90
J. 98
Answer: G
The natural water content of the granite residual soil sample is $w = 30.6\%$, the liquid limit of fine-grained soil with particle size less than 0.5mm is $w_{\mathrm{L}} = 50\%$, and the plastic limit is $w_{\mathrm{P}} = 30\%$. The percentage of particle mass with particle size greater than 0.5mm is $P_{0.5} = 40\%$. Which of the following options is closest to the liquidity index $I_{\mathrm{L}}$ of this soil sample?

Options:
A. 0.800
B. 1.140
C. 1.245
D. 0.540
E. 0.645
F. 0.970
G. 0.885
H. 0.715
I. 0.630
J. 0.590
Answer: G
The structure uses an independent square footing under the column, with the foundation's base dimensions being $2.4 \mathrm{m} \times 2.4 \mathrm{m}$, and the column's cross-sectional dimensions being $0.4 \mathrm{m} \times 0.4 \mathrm{m}$. The axial force acting at the center of the top of the foundation is $F = 700 \mathrm{kN}$, with the moment $M = 0$. According to the "Code for Design of Building Foundation" (GB 50007-2002), which of the following values is closest to the design value of the bending moment at the edge of the column section of the foundation?

Options:
A. 94.15kN·m
B. 96.68kN·m
C. 98.32kN·m
D. 108.66kN·m
E. 100.47kN·m
F. 115.89kN·m
G. 110.29kN·m
H. 120.56kN·m
I. 105.73kN·m
J. 92.45kN·m
Answer: I
The width of the raft foundation is 10m, with an embedment depth of 5m. The subsoil is a thick layer of homogeneous silt, and the groundwater level is 20m below the ground surface. At the base elevation, a deep plate load test determined the characteristic value of the foundation bearing capacity as $f_{\mathrm{ak}} = 200 \, \mathrm{kPa}$. The unit weight of the subsoil is 19 kN/m³ (from the table, the correction coefficients for the foundation bearing capacity can be obtained as: $\eta_{\mathrm{b}} = 0.3 \,, \, \, \, \eta_{\mathrm{d}} = 1.5$ ). What is the value of the uniformly distributed pressure at the base of the raft foundation that exactly meets the design requirements for the foundation bearing capacity?

Options:
A. 217.1kPa
B. 250.3kPa
C. 190.8kPa
D. 230.6kPa
E. 210.2kPa
F. 239.9kPa
G. 205.4kPa
H. 229.4kPa
I. 180.7kPa
J. 200.5kPa
Answer: A
The foundation dimensions of a certain office building are $42 \mathrm{m} \times 30 \mathrm{m}$. A box foundation is used, with a depth of 8m below the outdoor ground surface. The average pressure at the base is $425 \mathrm{kN/m}^{2}$. The density of the soil layer in the site area is $20 \mathrm{kN/m}^{3}$. The groundwater level is 5.0m below the outdoor ground surface, and the density of the groundwater is $10 \mathrm{kN/m}^{3}$. The ratio of the additional stress to the effective self-weight stress of the soil at a depth of 18m below the center point of the foundation base is ( ).

Options:
A. 0.90
B. 0.70
C. 0.85
D. 0.75
E. 0.45
F. 0.65
G. 0.55
H. 0.60
I. 0.50
J. 0.80
Answer: F
Given that the standard value of axial force at the ±0.00 elevation of the strip foundation under the wall is $F=400 \mathrm{kN/m}$, with a burial depth of 2.65m and an indoor-outdoor height difference of 0.45m, the corrected characteristic value of the foundation bearing capacity is $f_{\mathrm{a}}=160 \mathrm{kN/m}^{2}$. The base of the foundation uses concrete with a thickness of $H_{0}=300 \mathrm{mm}$, and above it is a rubble concrete foundation with a wall thickness of $360 \mathrm{mm}$. The height of the rubble concrete should be at least ()m. When the step width-to-height ratio is $\frac{1}{2}$, the height of the brick foundation is ()mm.

Options:
A. 1.70,560
B. 1.96,640
C. 1.92,650
D. 1.68,570
E. 1.80,590
F. 1.76,580
G. 1.72,580
H. 1.90,630
I. 1.88,620
J. 1.84,600
Answer: J
The piles used in a certain construction project are cast-in-place piles, with a pile diameter of 0.8m and an embedded depth of $L=28 \mathrm{m}$. The reinforcement of the pile body is $12φ16$, using C30 concrete. The proportional coefficient for the horizontal resistance of the soil around the pile is $m=14 \mathrm{MN/m}^{4}$. Known conditions: the elastic modulus of C30 concrete is $30.0 \times 10^{4} \mathrm{N/mm}^{2}$, the design tensile strength value is $f_{1}=1430 \mathrm{kN/m}^{2}$, and the elastic modulus of the steel is $2.0 \times 10^{5} \, \mathrm{N/mm}^{2}$. Assuming a vertical force at the pile top $N=2584 \mathrm{kN}$, then its characteristic value for the single pile horizontal bearing capacity is close to ( )kN.

Options:
A. 183.5kN
B. 205.7kN
C. 199.4kN
D. 224.8kN
E. 187.3kN
F. 231.6kN
G. 212.5kN
H. 193.6kN
I. 176.2kN
J. 218.9kN
Answer: C
For a certain concrete cast-in-place pile, it is known that the pile diameter is 0.8m, and the top of the pile is located 2.0m below the ground surface. The pile has a length of 10.0m and penetrates into the sand and gravel layer to a depth of $2 \mathrm{m}$. The stratigraphic conditions of the construction site are as follows:
First layer: $0-2 \mathrm{m}$, fill layer, unit weight $\gamma=18 \mathrm{kN/m}^{3}$; second layer: $2-4 \mathrm{m}$, silt, unit weight $\gamma=20 \mathrm{kN/m}^{3}$; third layer: $4-7 \mathrm{m}$, silty clay layer, unit weight $\gamma=20.2 \mathrm{kN/m}^{3}$, liquidity index $I_{\mathrm{L}}=1.0$; fourth layer: $7-10 \mathrm{m}$, clay layer, unit weight $\gamma=19 \mathrm{kN/m}^{3}$, liquidity index $I_{\mathrm{L}}=0.7$; fifth layer: below 10m, sand and gravel layer. After the groundwater level drops from -2.0m to -7.0m, the downward load caused by the negative skin friction on a single pile is () kN.

Options:
A. 450.9kN
B. 481.2kN
C. 485.8kN
D. 512.7kN
E. 459.4kN
F. 488.1kN
G. 479.5kN
H. 498.3kN
I. 465.6kN
J. 472.1kN
Answer: E
The plan is to reinforce a 10.0 m thick layer of silt using the preloading method. It is known that a 1.0 m thick layer of medium-coarse sand is laid on the silt surface, covered by an additional 2.0 m of compacted fill. The groundwater level is level with the top of the sand layer. The triaxial consolidated undrained test for the silt provides cohesion $\mathbf{c}_{\mathrm{eu}}=10.0 \mathbf{kPa}$ and an internal friction angle $\varphi_{\mathrm{vu}}=9.5°$. The natural shear strength at the silt surface is $\tau_{0}=12.3 \mathrm{kPa}$. The unit weight of the medium-coarse sand is 20 kN/m³, and the unit weight of the fill is 18 kN/m³. According to the Chinese "Technical Code for Ground Treatment of Buildings" (JGJ 79-2002), to increase the shear strength at the silt surface by 50%, what is the minimum required degree of consolidation?

Options:
A. 77%
B. 80%
C. 83%
D. 79%
E. 78%
F. 75%
G. 82%
H. 85%
I. 81%
J. 76%
Answer: B
The distribution of certain soft soil foundation layers and each soil layer is known, with a foundation burial depth of 2.0m. A composite foundation with mixing piles is adopted, with the mixing pile length being $10.0 \mathrm{m}$, pile diameter 500mm, and single pile bearing capacity of 120kN. To achieve a composite foundation bearing capacity of 180kPa, using a square pile arrangement, which of the following options for pile spacing is more appropriate (assuming the correction factor for the bearing capacity of the soil between piles, β=0.5)?

Options:
A. 0.85m
B. 1.15m
C. 0.70m
D. 0.75m
E. 1.05m
F. 0.65m
G. 0.90m
H. 1.00m
I. 0.80m
J. 0.95m
Answer: A
Known site conditions with soft clayey soil are treated using the high-pressure jet grouting method, with square pile arrangements. The pile diameter is 0.6m, the pile length is 12m, and the spacing between piles is 2.0m. The single pile bearing capacity determined by the strength of the soil around the pile is 800kN, and the characteristic value of the soil bearing capacity between piles is 110kPa. The reduction factor is 0.5. It is required that the composite foundation bearing capacity should not be less than 240kPa. The pile strength $f_{cu}$ is () MPa.

Options:
A. 8175.2kPa
B. 9100.2kPa
C. 7300.7kPa
D. 8500.1kPa
E. 7250.4kPa
F. 7800.6kPa
G. 8600.9kPa
H. 7900.8kPa
I. 9200.3kPa
J. 8000.5kPa
Answer: A
A vertical soil nail wall slope with soil nails at an angle of 15° to the horizontal plane has both horizontal and vertical spacings of 1.2m. The foundation soil behind the wall has $c = 15 \, \mathrm{kPa}$, $\varphi = 20°$, and $\gamma = 19 \, \mathrm{kN/m}^{3}$, with no surface surcharge. At a depth of 9.6m, which of the following options is closest to the axial tensile load on each soil nail?

Options:
A. 101.97kN
B. 95.19kN
C. 98.43kN
D. 92.75kN
E. 111.41kN
F. 87.06kN
G. 103.58kN
H. 105.32kN
I. 113.64kN
J. 108.88kN
Answer: A
A certain 30m-high rolled earth-rock dam has a water-facing slope with a slope ratio of 1:3. The relative density of the riprap is $2.4 \, \text{t/m}^3$, and the average wavelength of the reservoir water is $10 \, \text{m}$. When the cumulative frequency is 5%, the slope height is $2.0 \, \text{m}$. The suitable thickness of the riprap is ()m.

Options:
A. 0.900m
B. 0.800m
C. 1.150m
D. 0.512m
E. 0.750m
F. 0.648m
G. 1.025m
H. 0.375m
I. 0.560m
J. 0.475m
Answer: D