MikaStars39/nano-eval huggingface dataset:
Imagine there is a tunnel passing through the center of the Earth. It is known that the gravitational force experienced by a particle inside the Earth is proportional to the distance from the particle to the Earth's center, and the direction of the force points towards the center. A small ball is released into the tunnel from the Earth's surface without any initial velocity. Determine the motion of the ball along this tunnel. Given that the Earth's radius is $R = 6.37 \times 10^{6} \mathrm{~m}$ and the gravitational acceleration at the Earth's surface is $g = 9.8 \ \mathrm{m/s^2}$.What is the velocity of the ball as it passes through the center of the Earth and the time it takes to reach the center ?

Options:
A. The distance from the small ball to the center of the Earth changes according to the following rule $x=R \operatorname{csc} {\sqrt{\frac{g}{R}}} t, v=9.0 \times 10^{3} \ \mathrm{m/s}, T=1450 \mathrm{~s}=24.2 \mathrm{~min} \,.$
B. The distance from the small ball to the center of the Earth changes according to the following rule $x=R \operatorname{log} {\sqrt{\frac{g}{R}}} t, v=6.5 \times 10^{3} \ \mathrm{m/s}, T=1150 \mathrm{~s}=19.2 \mathrm{~min} \,.$
C. The distance from the small ball to the center of the Earth changes according to the following rule $x=R \operatorname{tan} {\sqrt{\frac{g}{R}}} t, v=7.6 \times 10^{3} \ \mathrm{m/s}, T=1250 \mathrm{~s}=20.8 \mathrm{~min} \,.$
D. The distance from the small ball to the center of the Earth changes according to the following rule $x=R \operatorname{sin} {\sqrt{\frac{g}{R}}} t, v=8.2 \times 10^{3} \ \mathrm{m/s}, T=1300 \mathrm{~s}= 21.7 \mathrm{~min} \,.$
E. The distance from the small ball to the center of the Earth changes according to the following rule $x=R \operatorname{cosh} {\sqrt{\frac{g}{R}}} t, v=7.7 \times 10^{3} \ \mathrm{m/s}, T=1200 \mathrm{~s}=20.0 \mathrm{~min} \,.$
F. The distance from the small ball to the center of the Earth changes according to the following rule $x=R \operatorname{sec} {\sqrt{\frac{g}{R}}} t, v=8.0 \times 10^{3} \ \mathrm{m/s}, T=1350 \mathrm{~s}=22.5 \mathrm{~min} \,.$
G. The distance from the small ball to the center of the Earth changes according to the following rule $x=R \operatorname{exp} {\sqrt{\frac{g}{R}}} t, v=5.0 \times 10^{3} \ \mathrm{m/s}, T=1000 \mathrm{~s}=16.7 \mathrm{~min} \,.$
H. The distance from the small ball to the center of the Earth changes according to the following rule $x=R \operatorname{sinh} {\sqrt{\frac{g}{R}}} t, v=8.5 \times 10^{3} \ \mathrm{m/s}, T=1400 \mathrm{~s}=23.3 \mathrm{~min} \,.$
I. The distance from the small ball to the center of the Earth changes according to the following rule $x=R \operatorname{cos} {\sqrt{\frac{g}{R}}} t, v=7.9 \times 10^{3} \ \mathrm{m/s}, T=1266.4 \mathrm{~s}=21.1 \mathrm{~min} \,.$
J. The distance from the small ball to the center of the Earth changes according to the following rule $x=R \operatorname{cot} {\sqrt{\frac{g}{R}}} t, v=6.0 \times 10^{3} \ \mathrm{m/s}, T=1100 \mathrm{~s}=18.3 \mathrm{~min} \,.$
Answer: I
A system with mass $m$ undergoes damped oscillations on a spring with stiffness $c$, under resistance $R$ proportional to velocity $R \left( R=\right)$ $T$. Given that ${\frac{n} {k}}=0.1$ (where $k^{2}=\frac{c} {m}, n=\frac{\alpha} {2 m}$), how many times is the period of the damped oscillation compared to the period of the undamped oscillation $T_{0}$?

Options:
A. $$
T \approx1. 0 0 1 T_{0}
$$
B. $$
T \approx1. 0 1 5 T_{0}
$$
C. $$
T \approx1. 0 0 3 T_{0}
$$
D. $$
T \approx0. 9 9 5 T_{0}
$$
E. $$
T \approx1. 0 0 5 T_{0}
$$
F. $$
T \approx1. 0 1 3 T_{0}
$$
G. $$
T \approx1. 0 0 8 T_{0}
$$
H. $$
T \approx1. 0 1 0 T_{0}
$$
I. $$
T \approx1. 0 2 0 T_{0}
$$
J. $$
T \approx0. 9 9 8 T_{0}
$$
Answer: E
The impact pendulum used to measure the bullet's speed consists of a cylinder $AB$ suspended on a horizontal axis $O$. One end of the cylinder $A$ is open, and the cylinder is filled with sand. The bullet, flying into the cylinder, causes the pendulum to rotate around the axis $O$ by an angle $\alpha$. It is known that the mass of the pendulum is $M$, and the distance from its center of mass to the axis $O$ is $OC = h$. The radius of gyration of the pendulum about the axis $O$ is $\rho$, and the mass of the bullet is $m$. The line of action of the collision impulse is at a distance $OD = a$ from the axis $O$. Assuming the pendulum axis $O$ does not experience the collision, meaning it satisfies $ah = \rho^{2}$.What is the speed of the bullet ?

Options:
A. $$
v=\frac{M+2 ( h+m a )} {m} \sqrt{\frac{g} {a}} \operatorname{s i n} \frac{\alpha} {2}
$$
B. $$
v=\frac{2 ( M a+m h )} {m} \sqrt{\frac{g} {h}} \operatorname{s i n} \frac{\alpha} {3}
$$
C. $$
v=\frac{2 ( m h+M a )} {M} \sqrt{\frac{g} {h}} \operatorname{s i n} \frac{\alpha} {2}
$$
D. $$
v=\frac{2 ( M+m a )} {h} \sqrt{\frac{g} {h}} \operatorname{s i n} \frac{\alpha} {2}
$$
E. $$
v=\frac{2 ( M h+m )} {M a} \sqrt{\frac{g} {h}} \operatorname{s i n} \frac{\alpha} {2}
$$
F. $$
v=\frac{2 ( m h+a M )} {M} \sqrt{\frac{a} {g}} \operatorname{s i n} \frac{\alpha} {2}
$$
G. $$
v=\frac{2 ( M h+m a )} {m} \sqrt{\frac{g} {a}} \operatorname{s i n} \frac{\alpha} {2}
$$
H. $$
v=\frac{2 ( M h+m a )} {M} \sqrt{\frac{g} {a}} \operatorname{tan} \frac{\alpha} {2}
$$
I. $$
v=\frac{2 ( M h+m )} {m a} \sqrt{\frac{h} {g}} \operatorname{s i n} \frac{\alpha} {2}
$$
J. $$
v=\frac{M ( h+m a )} {2 m} \sqrt{\frac{g} {a}} \operatorname{cos} \frac{\alpha} {2}
$$
Answer: G
Using an ionization chamber to measure the vapor of carbon-oxygen compounds containing $^{14}\text{C}$ (with a vapor pressure of 10 mmHg), the radioactivity is 1000 counts per minute. Afterward, it is burnt to form $\mathrm{CO_{2}}$ and measured using the same chamber (with a partial pressure of 40 mmHg) at 800 counts per minute. Assuming the counting efficiency of the chamber is the same in both cases, try to determine the number of carbon atoms in the organic compound molecule.

Options:
A. 1 carbon atom
B. 6 carbon atoms
C. 5 carbon atoms
D. 10 carbon atoms
E. 4 carbon atoms
F. 7 carbon atoms
G. 9 carbon atoms
H. 2 carbon atoms
I. 3 carbon atoms
J. 8 carbon atoms
Answer: C
In three weighing bottles, a small amount of thorium oxide, thorium nitrate, and argon thorium oxide are placed, respectively. Each sample is prepared to contain the same amount of thorium. Cover tightly with aluminum foil, and after one day, remove the aluminum and measure its radioactivity using a Geiger-Müller counter, yielding the following results:
The aluminum foil removed from the thorium oxide bottle shows a radioactivity of 131 counts per minute.
The aluminum foil removed from the argon thorium oxide bottle shows a radioactivity of 4520 counts per minute.
The aluminum foil removed from the thorium nitrate bottle shows a radioactivity of 246 counts per minute.
(The background radiation is 44 counts per minute.)
Calculate the radon escape coefficient. If the radon escape coefficient of argon thorium oxide is 80%, calculate the radon escape coefficients for thorium oxide and thorium nitrate using the experimental data mentioned above.

Options:
A. $$
1. 3 \% \quad5. 4 \%
$$
B. $$
0. 5 \% \quad7. 6 \%
$$
C. $$
2. 7 \% \quad4. 8 \%
$$
D. $$
1. 5 \% \quad3. 6 \%
$$
E. $$
0. 8 \% \quad4. 6 \%
$$
F. $$
1. 5 \% \quad6. 8 \%
$$
G. $$
2. 9 \% \quad5. 7 \%
$$
H. $$
3. 5 \% \quad2. 8 \%
$$
I. $$
2. 4 \% \quad3. 9 \%
$$
J. $$
3. 1 \% \quad5. 0 \%
$$
Answer: D
The thermal effect value of the reaction $\mathrm{H^{2}} ( d, n ) \mathrm{He}^{3}$ is 3.31 MeV (million electron volts), and the thermal effect of the reaction $\mathrm{H^{2} ( d, p ) H^{3}}$ is 3.98 MeV. Given that the mass difference for $( n, \mathrm{H} )$ corresponds to 0.75 MeV, determine the mass difference between $\mathbf{H^{3}}$ and He$^{3}$.

Options:
A. ~0.88 million electron volts
B. ~0.08 million electron volts
C. ~0.18 million electron volts
D. ~0.68 million electron volts
E. ~0.58 million electron volts
F. ~0.28 million electron volts
G. ~0.98 million electron volts
H. ~0.48 million electron volts
I. ~0.38 million electron volts
J. ~0.78 million electron volts
Answer: B
To study the efficiency of methods for grinding glass, some radium is added during the melting of the glass. Two glass samples of the same size are ground using different methods and processed with different types of materials. After grinding, both pieces of glass are placed in a British ionization chamber to measure the content of escaping radon gas. The first sample was kept in the ionization chamber for four days and four nights, resulting in an ionization current of $A_{1}$. The second sample was kept for one day and one night, with an ionization current of $\frac{1}{2}$ $A_{1}$. The question is, which glass is better ground, or which glass has a smaller true surface area?

Options:
A. The real area of the second glass sample is 15% larger, but it remains coarser.
B. The calculated surface of the first glass sample is 15% smaller, yet poorly polished.
C. The recorded area of the first glass sample is 40% smaller, leading to rougher edges.
D. The observed surface of the second glass sample is 29% larger, causing coarser texture.
E. The effective surface of the second glass sample is 20% larger, needing less smoothing.
F. The true surface of both glass samples is 29% larger, affecting performance.
G. The actual surface of the first glass sample is 29% smaller, but it is better polished.
H. The apparent surface of both glass samples is 5% larger, suggesting minor polishing.
I. The surface area of both glass samples is 50% larger, requiring less refinement.
J. The measured area of both glass samples is 10% larger, indicating smoother texture.
Answer: G
In radio astronomy, transitions between highly excited states of hydrogen atoms are observed, such as the transition from $n = 109$ to $n = 108$. Try to determine the wavelength and frequency of the radiation from this transition is____.

Options:
A. $$
2. 4 \mathrm{c m}
$$
$$
1. 8 5 \times1 0^{9} \mathrm{H z}
$$
B. $$
3. 3 \mathrm{c m}
$$
$$
7. 4 0 \times1 0^{9} \mathrm{H z}
$$
C. $$
8. 7 \mathrm{c m}
$$
$$
6. 5 0 \times1 0^{9} \mathrm{H z}
$$
D. $$
6. 5 \mathrm{c m}
$$
$$
3. 1 0 \times1 0^{9} \mathrm{H z}
$$
E. $$
0. 9 \mathrm{c m}
$$
$$
5. 7 5 \times1 0^{9} \mathrm{H z}
$$
F. $$
4. 9 \mathrm{c m}
$$
$$
2. 6 0 \times1 0^{9} \mathrm{H z}
$$
G. $$
5. 8 \mathrm{c m}
$$
$$
5. 1 5 \times1 0^{9} \mathrm{H z}
$$
H. $$
9. 4 \mathrm{c m}
$$
$$
8. 0 0 \times1 0^{9} \mathrm{H z}
$$
I. $$
7. 2 \mathrm{c m}
$$
$$
4. 3 0 \times1 0^{9} \mathrm{H z}
$$
J. $$
1. 1 \mathrm{c m}
$$
$$
9. 2 5 \times1 0^{9} \mathrm{H z}
$$
Answer: G
Directing a thermal neutron beam onto a crystal, the energy of the thermal neutrons can be determined from the Bragg diffraction pattern. If the atomic spacing of the crystal is 0.18 nm and the first-order Bragg grazing angle is 30°, calculate the energy of these neutrons.

Options:
A. $$
0. 2 0 9 ( \mathrm{e V} )
$$
B. $$
0. 0 2 5 ( \mathrm{e V} )
$$
C. $$
0. 0 4 8 ( \mathrm{e V} )
$$
D. $$
0. 0 1 3 ( \mathrm{e V} )
$$
E. $$
0. 0 6 4 ( \mathrm{e V} )
$$
F. $$
0. 1 5 2 ( \mathrm{e V} )
$$
G. $$
0. 1 8 5 ( \mathrm{e V} )
$$
H. $$
0. 0 5 7 ( \mathrm{e V} )
$$
I. $$
0. 0 3 1 ( \mathrm{e V} )
$$
J. $$
0. 0 4 0 ( \mathrm{e V} )
$$
Answer: B
Consider the homonuclear diatomic molecule $^{14} \mathrm{N}_{2}$. Given that the nuclear spin of nitrogen is $I=1$, attempt to derive the intensity ratio of two adjacent rotational spectral lines in the nitrogen molecule spectrum is___.

Options:
A. $$
8 : 5
$$
B. $$
7 : 5
$$
C. $$
9 : 4
$$
D. $$
3 : 2
$$
E. $$
4 : 3
$$
F. $$
6 : 1
$$
G. $$
5 : 3
$$
H. $$
1 : 2
$$
I. $$
3 : 1
$$
J. $$
2 : 1
$$
Answer: J
The binding energy of $^{90}_{40} Zr_{50}$ is 783.916 MeV, and the binding energy of $^{90}_{39}Y_{51}$ is 782.410 MeV. Estimate the lowest excitation energy of $^{90} Zr$ with isospin $T=6$ is___.

Options:
A. $$
6 4. 2 7 ( \mathrm{M e V} )
$$
B. $$
3 1. 6 0 ( \mathrm{M e V} )
$$
C. $$
0 2. 8 5 ( \mathrm{M e V} )
$$
D. $$
4 5. 7 2 ( \mathrm{M e V} )
$$
E. $$
9 9. 1 4 ( \mathrm{M e V} )
$$
F. $$
1 1. 5 9 ( \mathrm{M e V} )
$$
G. $$
7 6. 4 2 ( \mathrm{M e V} )
$$
H. $$
8 9. 3 1 ( \mathrm{M e V} )
$$
I. $$
1 8. 3 7 ( \mathrm{M e V} )
$$
J. $$
5 3. 0 8 ( \mathrm{M e V} )
$$
Answer: F
The average binding energy per nucleon of a deuterium nucleus is 1.11 MeV, and for a helium nucleus, it is 7.07 MeV. The energy released by the reaction $^{2}H+ ^{2}H→^{4}He$ is____.

Options:
A. $$
24.54 \mathrm{MeV}
$$
B. $$
26.11 \mathrm{MeV}
$$
C. $$
19.89 \mathrm{MeV}
$$
D. $$
22.67 \mathrm{MeV}
$$
E. $$
20.58 \mathrm{MeV}
$$
F. $$
28.65 \mathrm{MeV}
$$
G. $$
29.41 \mathrm{MeV}
$$
H. $$
21.73 \mathrm{MeV}
$$
I. $$
25.32 \mathrm{MeV}
$$
J. $$
2 3. 8 4 \mathrm{M e V}
$$
Answer: J
A battery can be in either a normal state or a failure state, with the probability of being in the normal state as $p.$ Let the electromotive force of a normal battery be 𝝴, and that of a failed battery be 0. There are $N$ batteries connected in series with a resistor. The average power dissipated by the resistor is____.

Options:
A. $$
\frac{1} {2R} \Big( 1+\frac{1-p} {N p} \Big) ( N p \varepsilon)^{2}
$$
B. $$
\frac{2} {R} \Big( 1+\frac{1-p} {N p} \Big) ( N p \varepsilon)^{2}
$$
C. $$
\frac{1} {R} \Big( 1+\frac{2-p} {N p} \Big) ( N p \varepsilon)^{2}
$$
D. $$
\frac{1} {R} \Big( 1-\frac{1-p} {N p} \Big) ( N p \varepsilon)^{2}
$$
E. $$
\frac{1} {R} \Big( 1+\frac{1-p} {N p} \Big) ( N p \varepsilon)
$$
F. $$
\frac{1} {R} \Big( 1+\frac{1-p} {N p} \Big) ( N p \varepsilon)^{2}
$$
G. $$
\frac{1} {R} \Big( 2+\frac{1-p} {N p} \Big) ( N p \varepsilon)^{2}
$$
H. $$
\frac{1} {R} \Big( 1+\frac{1-p} {N p^{2}} \Big) ( N p \varepsilon)^{2}
$$
I. $$
\frac{1} {R} \Big( 1+\frac{1-p} {2N p} \Big) ( N p \varepsilon)^{2}
$$
J. $$
\frac{1} {R} \Big( 1+\frac{1-p} {N p} \Big) ( N p \varepsilon)^{3}
$$
Answer: F
Consider an ideal lattice model with $N$ lattice sites and an equal number of vacancy sites (i.e., positions between lattice sites that atoms can also occupy). $E$ is the energy required to move an atom from a lattice site to a vacancy site. Let $n$ represent the number of atoms occupying vacancy sites at equilibrium.
(1) What is the internal energy of the system?
(2) What is the entropy of the system? (Provide the asymptotic expression for $n \gg 1$. )
(3) At temperature $T$, what is the $n$? ( Assume $n \gg 1$ ).

Options:
A. $$
U_{0} + 2n E.
$$
$$
k \big[ N \mathrm{l n} N-n \mathrm{l n} n-( N-n ) \mathrm{l n} ( N+n ) \big]
$$
$$
{\frac{N} {1+\mathrm{e}^{E / 2 k T}}}
$$
B. $$
U_{0}+n E.
$$
$$
2 k \big[ N \mathrm{l n} N-n \mathrm{l n} n-( N-n ) \mathrm{l n} ( N-n ) \big]
$$
$$
{\frac{N} {\mathrm{e}^{E / 2 k T}+1}}
$$
C. $$
U_{0} - n E.
$$
$$
2 k \big[ N \mathrm{l n} n-n \mathrm{l n} N-( N-n ) \mathrm{l n} ( n-N ) \big]
$$
$$
{\frac{N} {\mathrm{e}^{-E / 2 k T}+1}}
$$
D. $$
nE U_{0}.
$$
$$
2 k \big[ n \mathrm{l n} N-N \mathrm{l n} n-( N-n ) \mathrm{l n} ( N-n ) \big]
$$
$$
{\frac{2N} {\mathrm{e}^{E / 2 k T}+1}}
$$
E. $$
E(U_{0} + n).
$$
$$
2 k \big[ N \mathrm{l n} n-n \mathrm{l n} N+ ( N-n ) \mathrm{l n} n \big]
$$
$$
{\frac{N/2} {\mathrm{e}^{E / 2 k T}+1}}
$$
F. $$
U_{0} - n^2 E.
$$
$$
2 k \big[ N \mathrm{l n} N-n \mathrm{l n} n-( N-n ) \mathrm{l n} n \big]
$$
$$
{\frac{N} {\mathrm{e}^{E / k T}+2}}
$$
G. $$
U_{0}/n + E.
$$
$$
2 k \big[ (2N) \mathrm{l n} N-n \mathrm{l n} n-( N-n ) \mathrm{l n} ( N-n ) \big]
$$
$$
{\frac{2N} {1+\mathrm{e}^{E / 2 k T}}}
$$
H. $$
- U_{0}+n E.
$$
$$
2 k \big[ N \mathrm{l n} N-n \mathrm{l n} n- n\mathrm{l n} ( N-n ) \big]
$$
$$
{\frac{N} {\mathrm{e}^{E / k T}+1}}
$$
I. $$
U_{0} E- n.
$$
$$
2 k \big[ N \mathrm{l n} N-n \mathrm{l n} (2N)-( N-n ) \mathrm{l n} n \big]
$$
$$
{\frac{N} {\mathrm{e}^{E / k T/2}+1}}
$$
J. $$
U_{0} + n^2 E.
$$
$$
2k \big[ N \mathrm{l n} (2N)-n \mathrm{l n} n-( N-n ) \mathrm{l n} N \big]
$$
$$
{\frac{N} {\mathrm{e}^{E / k T}+1}}
$$
Answer: B
Consider a classical system at a temperature $T$ and volume $V$, consisting of $N$ particles each with a mass $m$. The total energy of the system is $U$, the pressure is $p$, and the interaction potential between particles is given by
$$
\phi( r_{i j} )=\frac{A} {r_{i j}^{n}}, \; \; \; A > 0, \; \; \; n > 0, \; \; \; | r_{i j} |=| r_{i}-r_{j} |
$$
Note that $\phi( \gamma_{r} ) \!=\! \gamma^{-n} \phi( r )$ holds for any $\gamma$. From this, prove that
$$
U = a p V + b V k T
$$
where $k$ is the Boltzmann constant, $a$ and $b$ are constants related to $n$. What are the $a$ and $b$ ?

Options:
A. $$
{\frac{2} {n}}
$$
$$
2 {\Big(} {\frac{1} {2}}+{\frac{1} {n}} {\Big)}
$$
B. $$
{\frac{6} {n}}
$$
$$
1 {\Big(} {\frac{1} {2}}-{\frac{1} {n-1}} {\Big)}
$$
C. $$
{\frac{3} {m}}
$$
$$
3 {\Big(} {\frac{1} {4}}-{\frac{1} {n}} {\Big)}
$$
D. $$
{\frac{3} {2n}}
$$
$$
2 {\Big(} {\frac{1} {2}}-{\frac{1} {n}} {\Big)}
$$
E. $$
{\frac{4} {n}}
$$
$$
2 {\Big(} {\frac{1} {3}}-{\frac{1} {n}} {\Big)}
$$
F. $$
{\frac{5} {n+1}}
$$
$$
1 {\Big(} {\frac{1} {2}}-{\frac{2} {n}} {\Big)}
$$
G. $$
{\frac{3} {n}}
$$
$$
3 {\Big(} {\frac{1} {2}}-{\frac{1} {n}} {\Big)}
$$
H. $$
{\frac{3} {n}}
$$
$$
4 {\Big(} {\frac{1} {2}}-{\frac{2} {n}} {\Big)}
$$
I. $$
{\frac{3} {n+1}}
$$
$$
3 {\Big(} {\frac{2} {3}}-{\frac{1} {n}} {\Big)}
$$
J. $$
{\frac{4} {n-1}}
$$
$$
2 {\Big(} {\frac{1} {3}}-{\frac{1} {n}} {\Big)}
$$
Answer: G
A cylindrical container holds a classic ideal gas, with the gas pressure at $p_{1}$ and temperature at $T_{1}$. The cylindrical container has a piston that can move up and down, with an area $A$ and a mass $M_{1}$. Thus, $\dot{p}_{1} \!=\! p_{0} \!+\! M_{1} g / A \,, p_{0}$ is the atmospheric pressure, and $g$ is the gravitational acceleration. A heavy object with a mass $M_{2}$ is suddenly placed on the piston, adiabatically compressing the gas to a new thermal equilibrium state. Assume the gas density is uniform and there is no frictional resistance during the piston's movement. What is the change in entropy of the gas ?

Options:
A. $$
N k \Big[ \frac{5} {2} \mathrm{l n} \Big( 1+\frac{2 M_{2}} {5 M_{1}} \Big)-\mathrm{l n} \Big( 1+\frac{M_{2}} {M_{1}} \Big) \Big]
$$
B. $$
N k \Big[ \frac{4} {3} \mathrm{l n} \Big( 1+\frac{3 M_{2}} {2 M_{1}} \Big)-\mathrm{l n} \Big( 1+\frac{M_{2}} {5 M_{1}} \Big) \Big]
$$
C. $$
N k \Big[ \mathrm{l n} \Big( 1+\frac{M_{2}} {5 M_{1}} \Big)-\frac{5} {4} \mathrm{l n} \Big( 1+\frac{3 M_{2}} {4 M_{1}} \Big) \Big]
$$
D. $$
N k \Big[ \frac{6} {3} \mathrm{l n} \Big( 1+\frac{M_{2}} {2 M_{1}} \Big)-\mathrm{l n} \Big( 1+\frac{2 M_{2}} {M_{1}} \Big) \Big]
$$
E. $$
N k \Big[ \frac{3} {2} \mathrm{l n} \Big( 1+\frac{3 M_{2}} {5 M_{1}} \Big)-\mathrm{l n} \Big( 1+\frac{M_{2}} {2 M_{1}} \Big) \Big]
$$
F. $$
N k \Big[ \mathrm{l n} \Big( 1+\frac{M_{2}} {M_{1}} \Big)-\frac{2} {3} \mathrm{l n} \Big( 1+\frac{2 M_{2}} {M_{1}} \Big) \Big]
$$
G. $$
N k \Big[ \mathrm{l n} \Big( 1+\frac{4 M_{2}} {3 M_{1}} \Big)-\frac{5} {2} \mathrm{l n} \Big( 1+\frac{M_{2}} {4 M_{1}} \Big) \Big]
$$
H. $$
N k \Big[ \frac{4} {5} \mathrm{l n} \Big( 1+\frac{2 M_{2}} {M_{1}} \Big)-\mathrm{l n} \Big( 1+\frac{M_{2}} {3 M_{1}} \Big) \Big]
$$
I. $$
N k \Big[ \frac{7} {4} \mathrm{l n} \Big( 1+\frac{M_{2}} {4 M_{1}} \Big)-\mathrm{l n} \Big( 1+\frac{2 M_{2}} {3 M_{1}} \Big) \Big]
$$
J. $$
N k \Big[ \frac{5} {3} \mathrm{l n} \Big( 1+\frac{M_{2}} {M_{1}} \Big)-\mathrm{l n} \Big( 1+\frac{3 M_{2}} {5 M_{1}} \Big) \Big]
$$
Answer: A
The temperature of a surface is 800°C. When sodium atoms evaporate from this surface, the number of sodium ions outside the surface is one hundred times the number of sodium atoms. When chlorine atoms evaporate from the same surface, the number of chlorine atoms outside the surface is one million times the number of chloride ions. The ionization potential of Na is $\Phi = 5.1 \mathrm{V}$. What is the electron affinity of chlorine ?

Options:
A. $$
3. 5 0 \mathrm{V}
$$
B. $$
4. 2 5 \mathrm{V}
$$
C. $$
3. 8 5 \mathrm{V}
$$
D. $$
4. 7 0 \mathrm{V}
$$
E. $$
2. 9 5 \mathrm{V}
$$
F. $$
7. 8 0 \mathrm{V}
$$
G. $$
4. 9 0 \mathrm{V}
$$
H. $$
6. 1 0 \mathrm{V}
$$
I. $$
5. 2 0 \mathrm{V}
$$
J. $$
5. 6 5 \mathrm{V}
$$
Answer: B
The subset of engineering works that require a separately prepared construction plan is ().

Options:
A. The construction of modular temporary housing excludes consideration for insulation panels.
B. The sheathing around underground utility lines is laid last to ensure waterproofing.
C. The installation of solar panels on public buildings is mandatory within two months of opening.
D. The scaffolding erected for high-rise steel structures remains until cladding is complete.
E. The assessment of fire exits in skyscrapers occurs only post full construction phase.
F. The grading of slope terraces is not adjusted to accommodate natural weather erosion.
G. The excavation plan for tunnel systems is finalized post environmental impact assessment.
H. The foundation of prefabricated composite bridges is inspected annually for safety compliance.
I. The design for earthquake-resistant piers requires real-time shock absorption systems.
J. The formwork beneath the post-tensioned prestressed concrete structure is completely removed before tensioning.
Answer: J
The contract price for a certain project is 15 million yuan, with a construction period of 312 days. The advance payment for the project is 25% of the contract price. The proportion of major materials and equipment is 60%. Therefore, the threshold for deducting the advance payment is () million yuan.

Options:
A. 975
B. 925
C. 1050
D. 850
E. 650
F. 800
G. 900
H. 700
I. 875
J. 1150
Answer: I
For a certain high-voltage electrical equipment with $\tan \delta = 0.01$, and a capacitance of $3500 \, \mathrm{pF}$, when an AC voltage of 50kV is applied, what should be the values of the components in the equivalent circuit when the insulation is represented by a series equivalent circuit and a parallel equivalent circuit, respectively?

Options:
A. $$
\frac{1 0^{1 0}} {3 5 \pi},~\frac{1 0^{6}} {3 5 \pi}
$$
B. $$
\frac{5 0^{1 0}} {3 5 \pi},~\frac{5 0^{6}} {3 5 \pi}
$$
C. $$
\frac{2 0^{1 0}} {3 5 \pi},~\frac{2 0^{6}} {3 5 \pi}
$$
D. $$
\frac{3 0^{1 0}} {3 5 \pi},~\frac{3 0^{6}} {3 5 \pi}
$$
E. $$
\frac{1 0^{1 0}} {4 5 \pi},~\frac{1 0^{6}} {4 5 \pi}
$$
F. $$
\frac{1 5^{1 0}} {3 5 \pi},~\frac{1 5^{6}} {3 5 \pi}
$$
G. $$
\frac{1 0^{1 0}} {7 0 \pi},~\frac{1 0^{6}} {7 0 \pi}
$$
H. $$
\frac{1 0^{9}} {3 5 \pi},~\frac{1 0^{5}} {3 5 \pi}
$$
I. $$
\frac{1 0^{1 0}} {5 0 \pi},~\frac{1 0^{6}} {5 0 \pi}
$$
J. $$
\frac{1 0^{1 0}} {6 0 \pi},~\frac{1 0^{6}} {6 0 \pi}
$$
Answer: A
In a 220kV level terminal substation, the impulse withstand level of the transformer is $U_{j}=945 \mathrm{kV}$, and the residual voltage of the valve-type surge arrester under 5kA is $U_{5}=630 \mathrm{kV}$. Given the steepness of the incoming wave $a = 300 \mathrm{kV} / \mu\mathrm{s}$, what is the maximum allowable electrical distance $l_{m}$ from the arrester to the transformer?

Options:
A. $$162.0~\mathrm{m}
$$
B. $$165.0~\mathrm{m}
$$
C. $$163.5~\mathrm{m}
$$
D. $$157.5~\mathrm{m}
$$
E. $$160.5~\mathrm{m}
$$
F. $$150.5~\mathrm{m}
$$
G. $$154.5~\mathrm{m}
$$
H. $$149.0~\mathrm{m}
$$
I. $$152.0~\mathrm{m}
$$
J. $$158.0~\mathrm{m}
$$
Answer: D
The International Practical Temperature Scale (1990) stipulates: The standard measuring instrument used from 13.803 $\mathbf{K}$ (the triple point of equilibrated hydrogen) to 961.78°C (the freezing point of silver at 0.101 MPa) is the platinum resistance thermometer. Let the resistance of the platinum at 0° and at a temperature of $\boldsymbol{t}$ be $R_{0}$ and $R(t)$ respectively, with $W(t) = {\frac{R(t)}{R_{0}}}$ defined. The functional relationship of $W(t)$ with $t$ is different in various temperature measurement ranges. Within the above measurement range, it is approximately:
$$
W(t) = 1 + At + Bt^{2}.
$$
If at 0.101 MPa, the resistance values corresponding to the melting point of ice, the boiling point of water, and the boiling point of sulfur (at a temperature of $444.67 \ \mathrm{°C}$) are 11.000 $\Omega$, 15.247 $\Omega$, and 28.887 $\Omega$, respectively, what are the constants $A$ and $B$ in the above formula ?

Options:
A. $$
6. 3 4 5 \, \times\, 1 0^{-3} (°C)^{-1} \,, \, \, \, 0. \, 5 6 7 \, \times\, 1 0^{-7} ( °C)^{-2}.
$$
B. $$
2. 7 7 7 \, \times\, 1 0^{-3} (°C)^{-1} \,, \, \, \, -\, 3. \, 9 9 9 \, \times\, 1 0^{-7} ( °C)^{-2}.
$$
C. $$
4. 6 5 4 \, \times\, 1 0^{-3} (°C)^{-1} \,, \, \, \, -\, 1. \, 5 6 7 \, \times\, 1 0^{-7} ( °C)^{-2}.
$$
D. $$
2. 5 0 0 \, \times\, 1 0^{-3} (°C)^{-1} \,, \, \, \, 6. \, 3 3 3 \, \times\, 1 0^{-7} ( °C)^{-2}.
$$
E. $$
4. 3 2 1 \, \times\, 1 0^{-3} (°C)^{-1} \,, \, \, \, -\, 8. \, 7 5 4 \, \times\, 1 0^{-7} ( °C)^{-2}.
$$
F. $$
4. 8 1 2 \, \times\, 1 0^{-3} (°C)^{-1} \,, \, \, \, 1. \, 2 3 4 \, \times\, 1 0^{-7} ( °C)^{-2}.
$$
G. $$
3. 9 2 0 \, \times\, 1 0^{-3} (°C)^{-1} \,, \, \, \, -\, 5. \, 9 1 9 \, \times\, 1 0^{-7} ( °C)^{-2}
$$
H. $$
3. 0 9 9 \, \times\, 1 0^{-3} (°C)^{-1} \,, \, \, \, 2. \, 4 6 8 \, \times\, 1 0^{-7} ( °C)^{-2}.
$$
I. $$
1. 9 8 7 \, \times\, 1 0^{-3} (°C)^{-1} \,, \, \, \, 4. \, 1 1 1 \, \times\, 1 0^{-7} ( °C)^{-2}.
$$
J. $$
5. 0 0 0 \, \times\, 1 0^{-3} (°C)^{-1} \,, \, \, \, 7. \, 8 9 0 \, \times\, 1 0^{-7} ( °C)^{-2}.
$$
Answer: G
The speed of an extraction pump is $\omega=400 \text{ r} \cdot \text{min}^{-1}$ (revolutions per minute), and the pump can extract 20 L of gas per minute. Assume the volume of the container is $V=2.0 \text{ L}$. How much time will it take for the pressure inside the container to decrease from 0.101 MPa to 133 Pa ?
( assuming the temperature remains constant during the extraction process )

Options:
A. 60s
B. 90s
C. 30s
D. 70s
E. 100s
F. 41.4s
G. 110s
H. 80s
I. 20s
J. 50s
Answer: F
Using a piston-type vacuum pump to evacuate a container with volume $V$, if the volume of gas removed by the pump with each piston stroke is $\Delta V$, how many times must the piston reciprocate for the pressure in the container to decrease from $p_{0}$ to $p$?
( Assume the gas temperature remains constant throughout. )

Options:
A. $$
\frac{\lg\frac{\Delta V} {V}} {\lg\Big( 1-\frac{p_{0}} {p} \Big)}
$$
B. $$
\frac{\lg\frac{V} {\Delta V}} {\lg\Big( 1-\frac{p} {p_{0}} \Big)}
$$
C. $$
\frac{\ln\frac{p_{0}} {p}} {\ln\Big( 1+\frac{\Delta V} {V} \Big)}
$$
D. $$
\frac{\lg\left( \frac{p} {p_{0}} \right)} {\lg\Big( 1+\frac{V} {\Delta V} \Big)}
$$
E. $$
\frac{\lg\left( \frac{p_{0}} {\Delta V} \right)} {\lg\Big( 1-\frac{p} {V} \Big)}
$$
F. $$
\frac{\lg\frac{p} {\Delta V}} {\lg\Big( 1+\frac{p_{0}} {V} \Big)}
$$
G. $$
\frac{\lg\frac{p_{0}} {V}} {\lg\Big( 1-\frac{\Delta V} {p} \Big)}
$$
H. $$
\frac{\lg\left( 1-\frac{V} {p} \right)} {\lg\frac{\Delta V} {p_{0}}}
$$
I. $$
\frac{\lg\frac{V} {p_{0}}} {\lg\Big( 1+\frac{p} {\Delta V} \Big)}
$$
J. $$
\frac{\lg\left( 1+\frac{V} {\Delta V} \right)} {\lg\frac{p_{0}} {p}}
$$
Answer: C
An object with an initial temperature of $T_{i}$ is placed in a room with a constant temperature of $T_{0}$. It is cooled through convective and radiative heat transfer. This heat transfer process follows Newton's Law of Cooling:
$\stackrel{\cdot} {Q}=-\ h A ( \, T \,-\, T_{0} \, )$
where $A$ is the surface area of the object, and $h$ is a constant. Given that the specific heat capacity of the object is $C$ and its mass is $m$, what is the temperature of the object at time $t$ ?

Options:
A. $$
T_{0} \ +\ ( \ T_{i} \ -\ T_{0} ) \ \cdot\ \operatorname{e x p} \Bigl( \ \frac{h A t} {c m} \Bigr)
$$
B. $$
T_{0} \ +\ ( \ T_{i} \ -\ T_{0} ) \ \cdot\ \log \Bigl( \ -\ \frac{h A t} {c m} \Bigr)
$$
C. $$
T_{0} \ +\ ( \ T_{i} \ -\ T_{0} ) \ \cdot\ \operatorname{e x p} \Bigl( \ -\ \frac{A h t} {c m} \Bigr)
$$
D. $$
T_{0} \ +\ ( \ T_{i} \ \cdot\ T_{0} ) \ \cdot\ \operatorname{e x p} \Bigl( \ -\ \frac{h A t} {c m} \Bigr)
$$
E. $$
T_{0} \ -\ ( \ T_{i} \ -\ T_{0} ) \ \cdot\ \operatorname{e x p} \Bigl( \ -\ \frac{h A t} {c m} \Bigr)
$$
F. $$
T_{0} \ +\ ( \ T_{i} \ -\ T_{0} ) \ \cdot\ \sin \Bigl( \ -\ \frac{h A t} {c m} \Bigr)
$$
G. $$
T_{0} \ +\ ( \ T_{i} \ -\ T_{0} ) \ \div\ \operatorname{e x p} \Bigl( \ -\ \frac{h A t} {c m} \Bigr)
$$
H. $$
T_{0} \ +\ ( \ T_{i} \ -\ T_{0} ) \ \cdot\ \operatorname{e x p} \Bigl( \ -\ \frac{h A t} {c m} \Bigr)
$$
I. $$
T_{0} \ +\ ( \ T_{i} \ +\ T_{0} ) \ \cdot\ \operatorname{e x p} \Bigl( \ \frac{h A t} {c m} \Bigr)
$$
J. $$
T_{i} \ +\ ( \ T_{0} \ -\ T_{i} ) \ \cdot\ \operatorname{e x p} \Bigl( \ -\ \frac{h A t} {c m} \Bigr)
$$
Answer: H
The heating equipment that combines a heat engine with a heat pump is called a power heating system, wherein the power to drive the heat pump is provided by the work done by the heat engine burning fuel. The heat pump extracts heat from a natural reservoir or from groundwater and supplies it to the water in the heating system with a higher temperature. Meanwhile, the water in the heating system also serves as the cooling water for the heat engine. If 1 kg of fuel is burned, the heat obtained by the boiler is $H$, and the temperatures of the boiler, groundwater, and heating system water are 210°C, 15°C, and 60°C, respectively. Assuming both the heat engine and heat pump are reversible Carnot machines, what is the ideal amount of heat received by the heating system per 1 kg of fuel burned ? (neglecting all practical losses)

Options:
A. $$
\approx1.5 H
$$
B. $$
\approx4.5 H
$$
C. $$
\approx2.5 H
$$
D. $$
\approx3.5 H
$$
E. $$
\approx2 H
$$
F. $$
\approx4 H
$$
G. $$
\approx5 H
$$
H. $$
\approx0.5 H
$$
I. $$
\approx3 H
$$
J. $$
\approx1 H
$$
Answer: I
In certain diatomic molecules, the interaction force (radial force) between atoms $A$ and $B$ and the distance $r$ between their centers is described by the equation $F = -\frac{a}{r^{2}} + \frac{b}{r^{3}}$. When $F$ is positive, it represents a repulsive force; when $F$ is negative, it represents an attractive force. Both $a$ and $b$ are positive constants. Assume that the mass of $A$ is much larger than the mass $m$ of $B$, and in the absence of other external forces, $A$ can be considered approximately stationary in a certain inertial frame of reference. Give the period $T$ of the small oscillations of $B$ around the equilibrium position of the force .

Options:
A. $$
2 \pi\, \sqrt{\frac{b^{2} m} {a^{5}}}
$$
B. $$
2 \pi\, \sqrt{\frac{b a^{3}} {m^{2}}}
$$
C. $$
2 \pi\, \sqrt{\frac{b^{3} m} {a^{4}}}
$$
D. $$
2 \pi\, \sqrt{\frac{a^{4} m} {b^{3}}}
$$
E. $$
2 \pi\, \sqrt{\frac{m^{3} b} {a^{4}}}
$$
F. $$
2 \pi\, \sqrt{\frac{a^{3} m} {b^{4}}}
$$
G. $$
2 \pi\, \sqrt{\frac{b^{3} a} {m^{4}}}
$$
H. $$
2 \pi\, \sqrt{\frac{a^{5} m} {b^{2}}}
$$
I. $$
2 \pi\, \sqrt{\frac{a^{2} b} {m^{5}}}
$$
J. $$
2 \pi\, \sqrt{\frac{b^{4} m} {a^{3}}}
$$
Answer: C
The main shaft of the rotary triangular piston engine completes one power stroke per rotation. For a dual-cylinder rotary type gasoline engine, if the compression ratio is $\varepsilon = 9$, the chamber volume is $V_{0} = 0.9 \mathrm{~L}$, the main shaft speed is $n = 6600 \mathrm{~rad} / \mathrm{min}$, the average pressure exerted by the gas on the piston is $p = 5 \mathrm{~at}$ (technical atmosphere), and the mechanical efficiency is $\eta = 95\%$. Find:
How many times are its output power compared to the output power of a dual-cylinder four-stroke reciprocating gasoline engine with a speed of $n^{\prime} = 3300 \mathrm{~rad} / \mathrm{min}$ and a mechanical efficiency of $\eta^{\prime} = 90\%$ ?
( assuming all other data of the two engines are identical )

Options:
A. $$
2. 5 P^{\prime}
$$
B. $$
2. 1 P^{\prime}
$$
C. $$
1. 9 P^{\prime}
$$
D. $$
5. 3 P^{\prime}
$$
E. $$
5. 0 P^{\prime}
$$
F. $$
4. 8 P^{\prime}
$$
G. $$
3. 5 P^{\prime}
$$
H. $$
4. 2
$$
I. $$
3. 0 P^{\prime}
$$
J. $$
4. 5 P^{\prime}
$$
Answer: H
When a spring oscillator undergoes simple harmonic motion, its amplitude is $A$. What is the instantaneous displacement value when its kinetic energy equals its elastic potential energy?

Options:
A. $$
x={\frac{3A} {\sqrt{2}}}
$$
B. $$
x={\frac{A} {4\sqrt{2}}}
$$
C. $$
x={\frac{A\sqrt{2}} {3}}
$$
D. $$
x={\frac{A} {2}}
$$
E. $$
x={\frac{A} {\sqrt{3}}}
$$
F. $$
x={\frac{A\sqrt{2}} {2}}
$$
G. $$
x={\frac{A} {\sqrt{2}}}
$$
H. $$
x={\frac{A\sqrt{3}} {2}}
$$
I. $$
x={\frac{2A} {\sqrt{2}}}
$$
J. $$
x={\frac{A} {3\sqrt{2}}}
$$
Answer: G
A flexible thin steel wire, 2m long with a mass of $0.01 \ \mathrm{kg}$, is tensioned with a force of 10N. Determine: What is the fundamental frequency of the wire's free vibration? If the displacement amplitude at the center point of the wire is 0.02m when vibrating at the fundamental frequency, what is the total energy of the fundamental frequency vibration? What is the velocity amplitude at a point 0.5m from one end of the wire?

Options:
A. $$
f_{1}=1 3. 0 \ \mathrm{H z} ;4. 9 0 \times1 0^{-3} \ \mathrm{J} ;0. 9 4 5 \ \mathrm{m} / \mathrm{s}
$$
B. $$
f_{1}=1 2. 5 \ \mathrm{H z} ;3. 8 9 \times1 0^{-3} \ \mathrm{J} ;0. 8 7 1 \ \mathrm{m} / \mathrm{s}
$$
C. $$
f_{1}=9. 7 0 \ \mathrm{H z} ;6. 0 0 \times1 0^{-3} \ \mathrm{J} ;1. 1 5 9 \ \mathrm{m} / \mathrm{s}
$$
D. $$
f_{1}=0. 9 8 \ \mathrm{H z} ;5. 2 3 \times1 0^{-3} \ \mathrm{J} ;1. 0 0 7 \ \mathrm{m} / \mathrm{s}
$$
E. $$
f_{1}=1 0. 5 \ \mathrm{H z} ;5. 0 1 \times1 0^{-3} \ \mathrm{J} ;1. 0 2 5 \ \mathrm{m} / \mathrm{s}
$$
F. $$
f_{1}=1 1. 8 \ \mathrm{H z} ;4. 1 3 \times1 0^{-3} \ \mathrm{J} ;0. 9 8 6 \ \mathrm{m} / \mathrm{s}
$$
G. $$
f_{1}=1 1. 5 \ \mathrm{H z} ;4. 6 8 \times1 0^{-3} \ \mathrm{J} ;0. 9 1 2 \ \mathrm{m} / \mathrm{s}
$$
H. $$
f_{1}=1 1. 2 \ \mathrm{H z} ;4. 9 3 \times1 0^{-3} \ \mathrm{J} ;0. 9 9 3 \ \mathrm{m} / \mathrm{s}
$$
I. $$
f_{1}=1 4. 2 \ \mathrm{H z} ;4. 5 7 \times1 0^{-3} \ \mathrm{J} ;0. 9 2 8 \ \mathrm{m} / \mathrm{s}
$$
J. $$
f_{1}=1 1. 0 \ \mathrm{H z} ;5. 0 3 \times1 0^{-3} \ \mathrm{J} ;1. 0 1 2 \ \mathrm{m} / \mathrm{s}
$$
Answer: H
A circular membrane with a radius of $0.015 \mathrm{~m}$ is fixed at the perimeter. Assuming its surface density is $\rho_{\mathrm{s}} = 2 \, \mathrm{kg/m}^{2}$, what is the minimum tension required for its fundamental frequency to be below 5000 Hz?

Options:
A. $$
T \,=\, 6. 3 8 \, \times\, 1 0^{4} \mathrm{~ N / m}
$$
B. $$
T \,=\, 5. 5 0 \, \times\, 1 0^{4} \mathrm{~ N / m}
$$
C. $$
T \,=\, 4. 0 4 \, \times\, 1 0^{4} \mathrm{~ N / m}
$$
D. $$
T \,=\, 3. 7 2 \, \times\, 1 0^{4} \mathrm{~ N / m}
$$
E. $$
T \,=\, 7. 2 5 \, \times\, 1 0^{4} \mathrm{~ N / m}
$$
F. $$
T \,=\, 8. 3 2 \, \times\, 1 0^{4} \mathrm{~ N / m}
$$
G. $$
T \,=\, 9. 1 5 \, \times\, 1 0^{4} \mathrm{~ N / m}
$$
H. $$
T \,=\, 8. 0 6 \, \times\, 1 0^{4} \mathrm{~ N / m}
$$
I. $$
T \,=\, 6. 9 0 \, \times\, 1 0^{4} \mathrm{~ N / m}
$$
J. $$
T \,=\, 7. 6 7 \, \times\, 1 0^{4} \mathrm{~ N / m}
$$
Answer: J
A strong ultrasound wave with a frequency of 10 MHz is applied to a tumor in soft tissue. Question: What is the wavelength of this ultrasound wave in air?

Options:
A. 0.50 mm, 1.8 mm
B. 0.35 mm, 1.2 mm
C. 0.45 mm, 1.4 mm
D. 0.34 mm, 1.5 mm
E. 0.40 mm, 1.6 mm
F. 0.36 mm, 1.0 mm
G. 0.60 mm, 1.7 mm
H. 0.48 mm, 1.1 mm
I. 0.38 mm, 1.3 mm
J. 0.32 mm, 1.9 mm
Answer: D
The density of the sandy seabed is $1,700 \ \mathrm{kg/m}^{3}$, and the sound speed is $1600 \ \mathrm{m/s}$. Try to determine: the critical angle for total internal reflection; at what angle of incidence is the sound power reflection coefficient equal to 0.25? (3) What is the sound power reflection coefficient at normal incidence?

Options:
A. $$
7 1 .1^{\circ} ;6 2^{\circ} ;0. 0 8 3
$$
B. $$
6 4 .4^{\circ} ;5 9^{\circ} ;0. 1 2 0
$$
C. $$
7 2 .2^{\circ} ;7 0^{\circ} ;0. 0 8 0
$$
D. $$
6 6 .6^{\circ} ;6 6^{\circ} ;0. 0 9 8
$$
E. $$
7 0 .0^{\circ} ;6 5^{\circ} ;0. 0 9 0
$$
F. $$
6 9 .9^{\circ} ;6 7^{\circ} ;0. 1 1 5
$$
G. $$
6 8 .8^{\circ} ;6 4^{\circ} ;0. 0 9 5
$$
H. $$
7 3 .3^{\circ} ;6 8^{\circ} ;0. 1 0 5
$$
I. $$
6 7. 7^{\circ} ;6 3^{\circ} ;0. 0 8 7
$$
J. $$
6 5. 5^{\circ} ;5 8^{\circ} ;0. 1 0 0
$$
Answer: I
A bubble with a radius $a$ equal to 0.1 cm undergoes harmonic pulsation at its natural frequency in water at 20°C, with a surface amplitude of $\xi_{0} \,=\, 0.01 \, a$. Try to calculate the radiation power of the bubble.

Options:
A. $$
6. 9 8 \times1 0^{-5} {\mathrm{~ W}}
$$
B. $$
7. 9 8 \times1 0^{-6} {\mathrm{~ W}}
$$
C. $$
7. 9 8 \times1 0^{-4} {\mathrm{~ W}}
$$
D. $$
7. 2 8 \times1 0^{-5} {\mathrm{~ W}}
$$
E. $$
7. 1 8 \times1 0^{-5} {\mathrm{~ W}}
$$
F. $$
7. 9 7 \times1 0^{-5} {\mathrm{~ W}}
$$
G. $$
8. 9 8 \times1 0^{-5} {\mathrm{~ W}}
$$
H. $$
9. 9 8 \times1 0^{-5} {\mathrm{~ W}}
$$
I. $$
5. 9 8 \times1 0^{-5} {\mathrm{~ W}}
$$
J. $$
7. 9 8 \times1 0^{-5} {\mathrm{~ W}}
$$
Answer: J
A microphone is placed in a free field where the sound pressure is 0.1 Pa. When the input impedance of the preamplifier is 50 $\Omega$, the output voltage at the preamplifier is measured to be $1.2 \mathrm{~mV}$. When the input impedance of the preamplifier is changed to 100 $\Omega$, the output voltage of the preamplifier becomes 2.3 mV. Assuming the amplification factor of the preamplifier remains unchanged and is equal to 10, calculate the free field voltage sensitivity of the microphone.

Options:
A. $$
2. 4 9 \times1 0^{-2} \mathrm{V / P a}
$$
B. $$
2. 5 0 \times1 0^{-2} \mathrm{V / P a}
$$
C. $$
2. 5 5 \times1 0^{-2} \mathrm{V / P a}
$$
D. $$
2. 8 3 \times1 0^{-2} \mathrm{V / P a}
$$
E. $$
2. 9 4 \times1 0^{-2} \mathrm{V / P a}
$$
F. $$
2. 7 6 \times1 0^{-2} \mathrm{V / P a}
$$
G. $$
3. 0 1 \times1 0^{-2} \mathrm{V / P a}
$$
H. $$
2. 6 7 \times1 0^{-2} \mathrm{V / P a}
$$
I. $$
2. 9 0 \times1 0^{-2} \mathrm{V / P a}
$$
J. $$
3. 1 8 \times1 0^{-2} \mathrm{V / P a}
$$
Answer: F
The equivalent width of the working gap of the playback head of a tape recorder is $1.0 \times 10^{-5}$ m. The recorded wavelength of the remanent magnetism on the tape is $2.0\times 10^{-5}$ m. Determine the gap loss of the playback head. What measures should be taken if we want to further reduce the gap loss of the playback head?

Options:
A. 5.7dB
B. 1.5dB
C. 5.0dB
D. 2.0dB
E. 3.3dB
F. 3.9dB
G. 2.8dB
H. 6.1dB
I. 4.5dB
J. 4.2dB
Answer: F
To find the absorption coefficient of seawater for a 50 kHz sound wave at a depth of 10 m, temperature of 20°C, and salinity of 35‰, and compare it with the situation in freshwater (salinity $s=0$, with other parameters being the same).

Options:
A. 12.0 dB/km; 0.75 dB/km.
B. 9.8 dB/km; 1.05 dB/km.
C. 10.5 dB/km; 1.75 dB/km.
D. 14.3 dB/km; 1.10 dB/km.
E. 10.9 dB/km; 0.80 dB/km.
F. 11.6 dB/km; 0.56 dB/km.
G. 12.5 dB/km; 0.62 dB/km.
H. 15.2 dB/km; 0.45 dB/km.
I. 13.7 dB/km; 0.67 dB/km.
J. 11.0 dB/km; 0.89 dB/km.
Answer: F
The speed of sound on the sea surface is 1500 m/s, and the sound speed gradient in the sea is constantly -0.1/s. The sonar transducer is at a depth of 10 m. When the transducer's depression angle is 4.5°, a target is found at a horizontal distance of 1000 m. Determine the target's depth.

Options:
A. 134m
B. 145m
C. 128m
D. 116m
E. 122m
F. 170m
G. 150m
H. 105m
I. 161m
J. 138m
Answer: E
A submarine has a speed of 3 kn, with the source level around 2 kHz being 110 dB (reference value 1 μPa). The sea state is level 4. The mixed layer thickness is 120 m. Using broadband detection, with a filter center frequency of 2 kHz and a bandwidth of 100 Hz. The hydrophone depth is 10 m, with a directivity index of 30 dB. The detection threshold is 0 dB. Determine the maximum distance at which the submarine can be detected.

Options:
A. 9.5km
B. 7.0km
C. 8.0km
D. 9.0km
E. 9.2km
F. 8.4km
G. 8.7km
H. 7.8km
I. 7.6km
J. 8.9km
Answer: F
A pilot in distress at sea drops a pound of explosives. Assuming it explodes on the deep water sound channel axis, determine the maximum distance at which the explosion can be heard. Suppose the receiving hydrophone is also located on the sound channel axis, is omnidirectional, and the environment is classified as sea state 4, with medium ship speed. The center frequency of the receiving system's passband is 200Hz, and the time interval for square-law integration of the signal is 2.0 seconds. The detection requirement is a signal-to-noise ratio of 10dB. The transition distance is 10,000 yards. The absorption coefficient is 0.0022dB/kiloyard.

Options:
A. 5200kyd.
B. 5900kyd.
C. 5800kyd.
D. 5100kyd.
E. 5600kyd.
F. 5500kyd.
G. 5000kyd.
H. 5700kyd.
I. 5400kyd.
J. 5300kyd.
Answer: J
The submarine travels in a straight line at a speed of 8 kn, while the frigate approaches from a bearing of 120° relative to the submarine's starboard at a speed of 30 kn. What is the Doppler relative frequency shift of the sonar echo received by the frigate from the submarine? If the carrier frequency of the sonar pulse is 5 kHz, what is the frequency shift? (1 n mile/h = 1 kn, 1 nautical mile = 1.83 km)

Options:
A. $\frac{∆f}{f}≈2‰$;15 Hz
B. $\frac{∆f}{f}≈3‰$;19 Hz
C. $\frac{∆f}{f}≈4‰$;22 Hz
D. $\frac{∆f}{f}≈10‰$;41 Hz
E. $\frac{∆f}{f}≈5‰$;25 Hz
F. $\frac{∆f}{f}≈1‰$;12 Hz
G. $\frac{∆f}{f}≈7‰$;31 Hz
H. $\frac{∆f}{f}≈8‰$;35 Hz
I. $\frac{∆f}{f}≈9‰$;38 Hz
J. $\frac{∆f}{f}≈6‰$;28 Hz
Answer: E
Determine the loudness level and loudness of a pure tone with a frequency of 100 Hz and an intensity level of 60 dB (relative to 1 pW/m²). To decrease the loudness obtained above to one-tenth, to what intensity level must the pure tone be reduced? If the loudness obtained in the first question is increased tenfold, to what intensity level will the pure tone be increased?

Options:
A. 5.5 sones; 50 dB (relative to 1 pW/m $^{2}$); 90 dB (relative to 1 pW/m $^{2}$)
B. 2.0 sones; 30 dB (relative to 1 pW/m $^{2}$); 88 dB (relative to 1 pW/m $^{2}$)
C. 1.8 sones; 35 dB (relative to 1 pW/m $^{2}$); 80 dB (relative to 1 pW/m $^{2}$)
D. 3.6 sones; 37 dB (relative to 1 pW/m $^{2}$); 81 dB (relative to 1 pW/m $^{2}$)
E. 3.3 sones; 45 dB (relative to 1 pW/m $^{2}$); 95 dB (relative to 1 pW/m $^{2}$)
F. 2.9 sones; 42 dB (relative to 1 pW/m $^{2}$); 86 dB (relative to 1 pW/m $^{2}$)
G. 1.5 sones; 33 dB (relative to 1 pW/m $^{2}$); 89 dB (relative to 1 pW/m $^{2}$)
H. 5.0 sones; 39 dB (relative to 1 pW/m $^{2}$); 92 dB (relative to 1 pW/m $^{2}$)
I. 2.7 sones; 40 dB (relative to 1 pW/m $^{2}$); 85 dB (relative to 1 pW/m $^{2}$)
J. 4.1 sones; 48 dB (relative to 1 pW/m $^{2}$); 82 dB (relative to 1 pW/m $^{2}$)
Answer: I
Between 100Hz and 300Hz, the noise spectral level of a factory relative to 20μPa/Hz $^{\frac{1}{2}}$ is 73dB. What is the minimum sound pressure level at which a 200Hz pure tone can be heard? Assume the critical ratio is effective.

Options:
A. 78dB
B. 88dB
C. 95dB
D. 98dB
E. 82dB
F. 90dB
G. 100dB
H. 105dB
I. 85dB
J. 92dB
Answer: F
A plane wave with a frequency of 40 kHz is propagating in freshwater at 5°C. How many decibels is this sound wave absorbed after traveling 4000 meters? If the medium is seawater at 5°C, what would the result be? (All calculations assume viscous absorption.)

Options:
A. 0.45 dB;0.42 dB
B. 0.70 dB;0.68 dB
C. 0.50 dB;0.48 dB
D. 0.65 dB;0.62 dB
E. 0.35 dB;0.33 dB
F. 0.48 dB;0.45 dB
G. 0.55 dB;0.52 dB
H. 0.60 dB;0.58 dB
I. 0.30 dB;0.28 dB
J. 0.40 dB;0.38 dB
Answer: A
A certain pure molybdenum-containing enzyme has an $a_{280}^{0.1\%}$ of 1.5 when measured with a 1 cm cuvette. The concentrated solution of this enzyme contains $10.56 \, \mu\mathrm{g} \, \mathrm{Mo} / \mathrm{ml}$. After a 1:50 dilution of this concentrated solution, the $A_{280 \, \mathrm{nm}}$ is 0.375. Calculate the minimum molecular weight of this enzyme is(). The atomic weight of $Mo$ is 95.94.

Options:
A. $$
\simeq1 8 0, 5 0 0
$$
B. $$
\simeq3 1 2, 4 0 0
$$
C. $$
\simeq2 0 5, 8 0 0
$$
D. $$
\simeq4 7, 1 0 0
$$
E. $$
\simeq5 7, 7 0 0
$$
F. $$
\simeq9 5, 9 4 0
$$
G. $$
\simeq8 9, 3 0 0
$$
H. $$
\simeq6 2, 1 0 0
$$
I. $$
\simeq1 1 3, 6 0 0
$$
J. $$
\simeq2 2 4, 2 0 0
$$
Answer: I
Accurately weigh 3.4 mg of pure proteolytic enzyme (with esterase activity) and treat it with an excess of diisopropyl fluorophosphate $^{-32}P(1 \mu\mathrm{~ C_{ i} / \mu\mathrm{m o l} ~}$). After 24 hours, add $KOH$ to the solution to decompose the unreacted (extremely toxic) $DF-^{32}P$ (diisopropyl fluorophosphate $-^{32}P$). Precipitate the labeled enzyme using trichloroacetic acid ($TCA$), wash away the free $^{32}P$, and then redissolve it in 0.5 ml of dilute $KOH$. Quantitatively transfer 0.5 ml to a scintillation counting vial for counting. When the counting efficiency is 80%, the count for the sample is 7380 counts per hour. Calculate the minimum molecular weight of the enzyme.

Options:
A. 49500
B. 45100
C. 52300
D. 48900
E. 47200
F. 46800
G. 36500
H. 47800
I. 44300
J. 46000
Answer: F
A solution mixture of 6-phosphoglucose and 1-phosphoglucose $1.0 mL$ is added with an excess of $NADP^{+}$, $MgCl_{2}$, and 6-phosphoglucose dehydrogenase solution $1.0 mL$. In a cuvette with a thickness of $1 cm$, the absorbance $A_{340 nm}$ increases to 0.57. When $A_{340 nm}$ no longer increases, $1.0 mL$ of phosphoglucomutase solution is added, reducing the absorbance to 0.50. Calculate the concentration of 1-phosphoglucose in the original solution.

Options:
A. $$
4. 5 2 \times1 0^{-5} M
$$
B. $$
4. 9 7 \times1 0^{-5} M
$$
C. $$
5. 1 6 \times1 0^{-5} M
$$
D. $$
7. 5 0 \times1 0^{-5} M
$$
E. $$
5. 0 3 \times1 0^{-5} M
$$
F. $$
6. 4 9 \times1 0^{-5} M
$$
G. $$
5. 7 9 \times1 0^{-5} M
$$
H. $$
6. 3 8 \times1 0^{-5} M
$$
I. $$
6. 8 4 \times1 0^{-5} M
$$
J. $$
7. 2 3 \times1 0^{-5} M
$$
Answer: G
The substrate concentration for a certain enzyme is $6 \times 10^{-4} M \, (K_{m} = 10^{-3} M)$, and the concentration of the non-competitive inhibitor is $2.5 \times 10^{-4} (K_{i} = 3 \times 10^{-5} M)$, with $V_{\mathrm{m}} = 515 \mathrm{n}M \times \mathrm{l}^{-1} \times \text{min}^{-1}$. Calculate the reaction rate of the enzyme and the percentage of inhibition.

Options:
A. 21.3 Nanomoles $\times$litres $^{-1}\times$cents $^{-1},81.5\%$
B. 24.1 Nanomoles $\times$litres $^{-1}\times$cents $^{-1},92.6\%$
C. 19.8 Nanomoles $\times$litres $^{-1}\times$cents $^{-1},67.4\%$
D. 18.5 Nanomoles $\times$litres $^{-1}\times$cents $^{-1},73.2\%$
E. 17.4 Nanomoles $\times$litres $^{-1}\times$cents $^{-1},70.0\%$
F. 16.7 Nanomoles $\times$litres $^{-1}\times$cents $^{-1},71.9\%$
G. 25.0 Nanomoles $\times$litres $^{-1}\times$cents $^{-1},95.8\%$
H. 22.9 Nanomoles $\times$litres $^{-1}\times$cents $^{-1},88.7\%$
I. 23.6 Nanomoles $\times$litres $^{-1}\times$cents $^{-1},94.1\%$
J. 20.7 Nanomoles $\times$litres $^{-1}\times$cents $^{-1},89.3\%$
Answer: J
Mix 1.7 mg of pure enzyme (molecular weight = 55000) with an excess of iodoacetamide $-^{14}C(S. A. =2\mu Ci/mmol)$ and incubate. Precipitate the carboxymethylated protein, wash away the unreacted iodoacetamide $-^{14}C$, and dissolve it in a small amount of buffer solution. Count the entire solution with a scintillation counter operating at 80% efficiency. Within 1 hour, the sample shows 13190 counts above background (exceeding the background). Calculate the number of reactive SH groups per protein molecule.

Options:
A. Each $3.09 \times 10^{-8} M$ of enzyme contains $5.00 \times 10^{-8} M$ of reduced thiol ($\text{one}\ \text{SH}$ or $\mathbf{Z}-\mathbf{S H}/M$).
B. Each $3.09 \times 10^{-8} M$ of enzyme contains $8.25 \times 10^{-8} M$ of reduced thiol ($\text{one}\ \text{SH}$ or $\mathbf{Z}-\mathbf{S H}/M$).
C. Each $3.09 \times 10^{-8} M$ of enzyme contains $6.19 \times 10^{-8} M$ of reduced thiol ($\text{one}\ \text{SH}$ or $\mathbf{Z}-\mathbf{S H}/M$).
D. Each $3.09 \times 10^{-8} M$ of enzyme contains $3.50 \times 10^{-8} M$ of reduced thiol ($\text{one}\ \text{SH}$ or $\mathbf{Z}-\mathbf{S H}/M$).
E. Each $3.09 \times 10^{-8} M$ of enzyme contains $5.20 \times 10^{-8} M$ of reduced thiol ($\text{one}\ \text{SH}$ or $\mathbf{Z}-\mathbf{S H}/M$).
F. Each $3.09 \times 10^{-8} M$ of enzyme contains $9.00 \times 10^{-8} M$ of reduced thiol ($\text{one}\ \text{SH}$ or $\mathbf{Z}-\mathbf{S H}/M$).
G. Each $3.09 \times 10^{-8} M$ of enzyme contains $4.50 \times 10^{-8} M$ of reduced thiol ($\text{one}\ \text{SH}$ or $\mathbf{Z}-\mathbf{S H}/M$).
H. Each $3.09 \times 10^{-8} M$ of enzyme contains $5.75 \times 10^{-8} M$ of reduced thiol ($\text{one}\ \text{SH}$ or $\mathbf{Z}-\mathbf{S H}/M$).
I. Each $3.09 \times 10^{-8} M$ of enzyme contains $7.00 \times 10^{-8} M$ of reduced thiol ($\text{one}\ \text{SH}$ or $\mathbf{Z}-\mathbf{S H}/M$).
J. Each $3.09 \times 10^{-8} M$ of enzyme contains $6.50 \times 10^{-8} M$ of reduced thiol ($\text{one}\ \text{SH}$ or $\mathbf{Z}-\mathbf{S H}/M$).
Answer: C
By using spectrophotometry to track changes in $NADH$ concentration, the activity of lactate dehydrogenase can be determined. The total volume of the assay system is $3.0ml$, containing sufficient lactate, buffer solution, $0.1ml$ of enzyme preparation, and semicarbazide (which binds with pyruvate to ensure the reaction completes). Each ml of enzyme preparation contains $120\mu g$ of protein. The increase in $A_{340 \mathrm{nm}}$ is 0.048 per minute. What is the concentration of lactate dehydrogenase in the preparation (units/ml)?

Options:
A. 0.198 units/ml
B. 0.241 units/ml
C. 0.232 units/ml
D. 0.215 units/ml
E. 0.289 units/ml
F. 0.267 units/ml
G. 0.276 units/ml
H. 0.225 units/ml
I. 0.249 units/ml
J. 0.219 units/ml
Answer: C