問題一覧
1
Which of the ff correctly describes the principle of least action in classical mechanics?
The trajectory of a particle is the one that extremizes the action Integral.
2
In classical mechanics, which of the following is a correct interpretation of Poisson brackets?
They determine whether two classical quantities are independent conserved quantities.
3
According to Liouville's theorem in classical mechanics, which of the following statements is correct?
The phase space volume of an ensemble of systems is conserved over time.
4
A block of mass m is placed on a frictionless horizontal surface and connected to a spring of force constant k. If the block is displaced by x0 and released, which of the following correctly describes its motion?
The block executes simple harmonic motion with angular frequency sqrt(k/m).
5
A car of mass m is moving along a circular track of radius R with constant speed v. What is the magnitude of the net force acting on the car?
mv³/R directed radially inward.
6
A harmonic oscillator with mass m and frequency w has total energy E. What is the maximum speed of the oscillator?
vmax= sqrt(2E / m)
7
A mass-spring system with mass m and spring constant k is driven by an external force F(t) = F * 0cos(omegat) At resonance, what is the system's oscillation frequency?
w = sqrt(k/m)
8
The frequency of vibration of a 1H35CI molecule is 8.966 x 1013 s-1. What would the frequency be if the hydrogen atom were infinitely massive?
v= 1.501 x1013s - 1
9
Which of the statements about classical wave motion is incorrect?
The amplitude of a wave is directly related to its frequency in all cases.
10
Which of the following types of waves requires a medium for propagation?
Sound waves
11
Which of the following is true about the Hamiltonlan function in classical mechanics?
It is the total energy of the system, expressed in terms of generalized coordinates and momenta.
12
A particle moves in a central force field with potential energy V(r)=-rk. What is the nature of its motion according to classical mechanics?
The motion can be either bounded (elliptical) or unbounded (parabolic/hyperbolic) depending on energy. The motion is completely independent of initial conditions.
13
A particle of mass m is moving under the influence of a force given by F=-kv, where k is a positive constant and v is the velocity of the particle. What is the velocity of the particle as a function of time if it starts with Initial velocity vo at t=0?
v(t) = v0e ^ (- kt / m)
14
Two bodies of masses m1 and m2 are connected by a massless string and suspended over a frictionless pulley. If m1 > m2, what is the acceleration of the system?
g (m1-m2/m1+m2)
15
The general solution of a one-dimensional classical harmonic oscillator with mass m and force constant k is given by x(t) = A * cos(omegat + phi) What is the correct expression for the angular frequency ω?
w= sqrt(k/m)
16
The potential energy function for a one-dimensional harmonic oscillator is given by V(x) = 1/2 k x ^ 2 what position does the kinetic energy equal the potential energy?
x = A / (sqrt(3))
17
The frequency of a 12C160 molecule is 6.5405 x 1013 s-1. The atomic masses are: 12C: 12.00000 amu; 13C: 13.00335 amu; 160: 15.994915 amu; 170: 16.99913 amu. Find the vibrational frequency of a 13C160 molecule, assuming that the force constant is unchanged.
v=6.401x10^13 s-1
18
Assume that a hydrogen atom is bonded to a large crystal with a chemical bond that is equivalent to a spring having a force constant equal to 600.0 N m-1. Assume that the hydrogen atom oscillates harmonically but the atom at the other end of the bond is stationary. Find the frequency of the oscillation.
v = 9.532 * 10115 - 1
19
A a medium has a frequency of 500 Hz and a wavelength of 2 m. What is its speed?
1000 m/s
20
For a sinusoidal wave traveling in a medium, which of the following properties remains unchanged when it moves from one medium to another?
Frequency
21
A standing wave is formed when:
Two waves of the same frequency and amplitude travel in opposite directions and interfere.
22
If a flexible string is stretched under tension T and has a mass per unit length µ, the speed of wave propagation along the string is given by:
v=vsqrt(T/u)
23
If the tension in a stretched string is quadrupled, how does the wave speed change?
It doubles.
24
A travelling wave is described by the equation: y(x,t) = Asin(kx-ot) What does the term k represent?
Angular wave number
25
A wave is travelling in the +x direction and is given by: y(x,t)=Asin(x+ut) What happens to the wave direction if the equation changes to: y(x,t)=Asin(lx-wt)
The wave reverses and moves in the -x direction.
26
A sinusoidal travelling wave moves in the +x direction with an amplitude of 0.05 m and a frequency of 20 Hz. If the wave speed is 5m / s_{0} what is its wavelength?
0.5 m
27
Which of the following correctly expresses the relationship between the speed of light c, its frequency f, and wavelength A?
c=λ/f
28
Which of the following correctly describes the nature of the oscillating electric and magnetic fields in an electromagnetic wave?
The electric and magnetic fields oscillate perpendicular to each other and perpendicular to the direction of propagation.
29
A violin string has a mass per unit length of 3gm - 1 Find the tension force necessary to produce a fundamental frequency s-1 if the length of the string is 50.0 cm.
T=585.1N
30
Which of the following is a direct consequence of Planck's quantization of energy?
Photoelectric effect
31
Which of the following observations in the photoelectric effect could not be explained by classical wave theory?
Both B and C
32
A flexible string of length L is fixed at both ends and vibrating in its fundamental mode. What is the wavelength of the wave formed on the string?
L/2
33
A string of length L is fixed at both ends and vibrates in the second harmonic mode. How many nodes and antinodes are present in the string?
3 nodes, 2 antinodes
34
A flexible string of length L is vibrating in the third harmonic mode. What is the frequency ratio between this mode and the fundamental mode?
1:3
35
The speed of a travelling wave is given by which equation
v=w/k
36
A wave on a string is described by: y(x,t)=0.02sin(5x-40t) What is the wave speed?
10 m/s
37
Which of the following statements about electromagnetic waves is incorrect?
Electromagnetic waves require a material medium for propagation.
38
In classical wave theory, what is the significance of the intensity of an electromagnetic wave?
It is proportional to the square of the electric field amplitude.
39
What happens to the wavelength of an electromagnetic wave when it from vacuum into a medium with refractive index n?
It decreases by a factor of n.
40
Which assumption in Planck's quantum hypothesis resolved the "ultraviolet catastrophe" in black-body radiation?
Energy is quantized as E-nhv, where n is an integer
41
The Stefan-Boltzmann law states that the total power radiated by a black body per unit area is proportional to:
T2
42
The work function ()of a metal represents:
The minimum photon energy required to eject an electron
43
A metal has a work function of 2.0 eV. If light of wavelength 400 nm is incident on it, what will be the maximum kinetic energy of the emitted electrons?
1.1 eV
44
Which of the following correctly expresses Einstein's photoelectric equation?
KEmax hv-
45
Which phenomenon best demonstrates the particle nature of light?
Photoelectric effect
46
In the Compton effect, when X-rays scatter off electrons, what happens to the wavelength of the X-ray photons?
It increases
47
In Bohr's model of the hydrogen atom, the quantization of electron orbits is based on which fundamental principle?
The angular momentum of the electron is an integer multiple of A (reduced Planck's constant)
48
What happens when an electron in a hydrogen atom transitions from a higher energy level (n) to a lower energy level (n.)?
A photon is emitted with energy hvwEn2-En1
49
The stopping potential in a photoelectric experiment is the potential required to:
Stop the most energetic emitted electrons from reaching the anode
50
Which of the following experimental observations provided the first direct evidence of the wave nature of light?
Double-slit experiment
51
According to de Broglie's hypothesis, the wavelength (A) associated with a moving particle of mass m and velocity v is given by
h/mv
52
Which of the following statements best describes wave-particle duality?
Light sometimes behaves as a wave and sometimes as a particle, depending on the experiment.
53
Which of the following correctly describes the radius of the electron's orbit in the hydrogen atom according to Bohr's model?
rnn2r0, where ro is the Bohr radius
54
Bohr's model successfully explains the spectral lines of hydrogen but fails for multi-electron atoms. Why?
It does not account for electron-electron interactions in multi-electron atoms