PHY 111 FINAL EXAM PRACTICE EVALUATION BANK
FULL SOLUTION SET - 121 Questions and Answers Already
Graded A+ Premium Exam Tested And Verified
Subject Area Physics
Description Comprehensive final exam covering classical mechanics, electromagnetism,
thermodynamics, waves, and modern physics. Emphasizes problem-solving,
conceptual understanding, and quantitative reasoning at the level of a rigorous
introductory physics sequence for science and engineering majors.
Expected Grade A+
Total Questions 121
Duration 3 hours
Learning Outcomes 1. Apply Newton's laws to complex systems including non-inertial frames
2. Analyze electromagnetic fields using Maxwell's equations in integral form
3. Solve thermodynamic cycles and interpret entropy changes
4. Use wave interference and diffraction principles to predict patterns
5. Relate quantum mechanical concepts to experimental observations
Accreditation ABET-accredited engineering program; meets standards for rigorous physics
foundation at top US research universities
Page 1
,1. A particle of mass m moves in one dimension under the influence of a potential
V(x) = k x^4, where k > 0. The particle is released from rest at x = A. Which of the
following correctly describes the period of oscillation T for small amplitudes?
A. T is independent of A
B. T is proportional to A^{-1}
C. T is proportional to A^{-1/2}
D. T is proportional to A^0 (constant)
Answer: B. T is proportional to A^{-1}
For a quartic potential, the period scales with amplitude as T A^{-1}. This can be
derived using conservation of energy and the integral for period: T = (2m) dx / (E - V),
where V x^4, leading to T A^{1 - n/2} with n=4, so T A^{-1}. Option C is for a
harmonic oscillator (n=2). Options A and D are incorrect.
2. A spherical balloon of radius R carries a uniform surface charge density . The
balloon is slowly inflated to radius 2R while maintaining the same total charge. How
does the electrostatic energy stored in the field change?
A. It increases by a factor of 2
B. It decreases by a factor of 2
C. It remains the same
D. It decreases by a factor of 4
Answer: B. It decreases by a factor of 2
The electrostatic energy of a charged sphere is U = Q^2/(80R). Since Q is constant, U
1/R. When R doubles, U halves. Thus the energy decreases by a factor of 2. Option D
would be for a factor of 4 change, which would require R to quadruple. Options A and
C are incorrect.
Page 2
,3. An ideal gas undergoes a reversible cycle consisting of an isothermal expansion at
temperature T1, followed by an adiabatic expansion to temperature T2, then an
isothermal compression at T2, and finally an adiabatic compression back to the
initial state. What is the efficiency of this cycle?
A. 1 - T2/T1
B. 1 - (T2/T1)^
C. 1 - (T2/T1)^(-1)
D. 1 - (T2/T1)^(1/)
Answer: A. 1 - T2/T1
This is a Carnot cycle, which consists of two isothermal and two adiabatic processes.
The efficiency of a Carnot engine is 1 - T_cold/T_hot = 1 - T2/T1. Options B, C, and D
include the adiabatic index incorrectly; the Carnot efficiency depends only on
temperatures.
4. Two coherent light sources emit waves of wavelength . The waves interfere at a
point P where the path difference is /4. What is the phase difference between the two
waves at P?
A. /2
B.
C. 2
D. /4
Answer: A. /2
Phase difference = (2/) × path difference. For path difference /4, = (2/)*(/4) = /2. Option
B corresponds to path difference /2, C to , D to /8.
Page 3
, 5. A photon of energy E strikes a free electron initially at rest. After scattering, the
photon's energy is E'. Which of the following is the maximum possible kinetic energy
of the electron?
A. E - E'
B. E
C. 2E
D. E/(1 + (mc^2)/(2E))
Answer: D. E/(1 + (mc^2)/(2E))
In Compton scattering, the maximum kinetic energy of the electron is given by K_max
= E * (2E/(mc^2)) / (1 + 2E/(mc^2)) = E/(1 + mc^2/(2E)). This occurs when the photon
is backscattered (=). Option A is the energy transferred, but not necessarily maximum.
Option B is the initial photon energy, which is not possible. Option C is too large.
6. A particle of mass m is confined in a one-dimensional infinite potential well of
width L. The particle is in the second excited state (n=3). What is the probability that
a measurement of its position finds it in the central third of the well (i.e., between L/3
and 2L/3)?
A. 1/3
B. 1/2
C. 1/3 + (1/(2)) sin(2/3)
D. 1/3 - (1/(2)) sin(2/3)
Answer: C. 1/3 + (1/(2)) sin(2/3)
The probability is ||^2 dx from L/3 to 2L/3. For n=3, = (2/L) sin(3x/L). The integral
yields 1/3 + (1/(2)) sin(2/3). Option D has a minus sign, which is incorrect. Options A
and B are classical approximations.
Page 4
FULL SOLUTION SET - 121 Questions and Answers Already
Graded A+ Premium Exam Tested And Verified
Subject Area Physics
Description Comprehensive final exam covering classical mechanics, electromagnetism,
thermodynamics, waves, and modern physics. Emphasizes problem-solving,
conceptual understanding, and quantitative reasoning at the level of a rigorous
introductory physics sequence for science and engineering majors.
Expected Grade A+
Total Questions 121
Duration 3 hours
Learning Outcomes 1. Apply Newton's laws to complex systems including non-inertial frames
2. Analyze electromagnetic fields using Maxwell's equations in integral form
3. Solve thermodynamic cycles and interpret entropy changes
4. Use wave interference and diffraction principles to predict patterns
5. Relate quantum mechanical concepts to experimental observations
Accreditation ABET-accredited engineering program; meets standards for rigorous physics
foundation at top US research universities
Page 1
,1. A particle of mass m moves in one dimension under the influence of a potential
V(x) = k x^4, where k > 0. The particle is released from rest at x = A. Which of the
following correctly describes the period of oscillation T for small amplitudes?
A. T is independent of A
B. T is proportional to A^{-1}
C. T is proportional to A^{-1/2}
D. T is proportional to A^0 (constant)
Answer: B. T is proportional to A^{-1}
For a quartic potential, the period scales with amplitude as T A^{-1}. This can be
derived using conservation of energy and the integral for period: T = (2m) dx / (E - V),
where V x^4, leading to T A^{1 - n/2} with n=4, so T A^{-1}. Option C is for a
harmonic oscillator (n=2). Options A and D are incorrect.
2. A spherical balloon of radius R carries a uniform surface charge density . The
balloon is slowly inflated to radius 2R while maintaining the same total charge. How
does the electrostatic energy stored in the field change?
A. It increases by a factor of 2
B. It decreases by a factor of 2
C. It remains the same
D. It decreases by a factor of 4
Answer: B. It decreases by a factor of 2
The electrostatic energy of a charged sphere is U = Q^2/(80R). Since Q is constant, U
1/R. When R doubles, U halves. Thus the energy decreases by a factor of 2. Option D
would be for a factor of 4 change, which would require R to quadruple. Options A and
C are incorrect.
Page 2
,3. An ideal gas undergoes a reversible cycle consisting of an isothermal expansion at
temperature T1, followed by an adiabatic expansion to temperature T2, then an
isothermal compression at T2, and finally an adiabatic compression back to the
initial state. What is the efficiency of this cycle?
A. 1 - T2/T1
B. 1 - (T2/T1)^
C. 1 - (T2/T1)^(-1)
D. 1 - (T2/T1)^(1/)
Answer: A. 1 - T2/T1
This is a Carnot cycle, which consists of two isothermal and two adiabatic processes.
The efficiency of a Carnot engine is 1 - T_cold/T_hot = 1 - T2/T1. Options B, C, and D
include the adiabatic index incorrectly; the Carnot efficiency depends only on
temperatures.
4. Two coherent light sources emit waves of wavelength . The waves interfere at a
point P where the path difference is /4. What is the phase difference between the two
waves at P?
A. /2
B.
C. 2
D. /4
Answer: A. /2
Phase difference = (2/) × path difference. For path difference /4, = (2/)*(/4) = /2. Option
B corresponds to path difference /2, C to , D to /8.
Page 3
, 5. A photon of energy E strikes a free electron initially at rest. After scattering, the
photon's energy is E'. Which of the following is the maximum possible kinetic energy
of the electron?
A. E - E'
B. E
C. 2E
D. E/(1 + (mc^2)/(2E))
Answer: D. E/(1 + (mc^2)/(2E))
In Compton scattering, the maximum kinetic energy of the electron is given by K_max
= E * (2E/(mc^2)) / (1 + 2E/(mc^2)) = E/(1 + mc^2/(2E)). This occurs when the photon
is backscattered (=). Option A is the energy transferred, but not necessarily maximum.
Option B is the initial photon energy, which is not possible. Option C is too large.
6. A particle of mass m is confined in a one-dimensional infinite potential well of
width L. The particle is in the second excited state (n=3). What is the probability that
a measurement of its position finds it in the central third of the well (i.e., between L/3
and 2L/3)?
A. 1/3
B. 1/2
C. 1/3 + (1/(2)) sin(2/3)
D. 1/3 - (1/(2)) sin(2/3)
Answer: C. 1/3 + (1/(2)) sin(2/3)
The probability is ||^2 dx from L/3 to 2L/3. For n=3, = (2/L) sin(3x/L). The integral
yields 1/3 + (1/(2)) sin(2/3). Option D has a minus sign, which is incorrect. Options A
and B are classical approximations.
Page 4
