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GT Students Final Quiz 2026-2027 BANK QUESTIONS WITH
DETAILED VERIFIED ANSWERS EXAM QUESTIONS WILL
COME FROM HERE (100% CORRECT ANSWERS A+ GRADED
1. In classical mechanics, if the net external force acting on a system of
particles is zero, which of the following quantities is necessarily
conserved?
A) Kinetic energy
B) Potential energy
C) Linear momentum
D) Angular momentum about an arbitrary point
Answer: C
Explanation: According to Newton's second law for a system of
particles, the net external force equals the time rate of change of total
linear momentum. If the net external force is zero, the derivative is
zero, implying that the total linear momentum vector is constant.
Kinetic energy may not be conserved if internal forces do work, and
angular momentum conservation requires zero net external torque, not
just zero force.
2. The Hamiltonian formulation of mechanics elegantly expresses the
equations of motion in terms of which two fundamental quantities?
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A) Generalized coordinates and velocities
B) Generalized coordinates and conjugate momenta
C) Time and action
D) Position and acceleration
Answer: B
Explanation: In Hamiltonian mechanics, the state of a system is
described by generalized coordinates q_i and their conjugate momenta
p_i. Hamilton's equations relate the time derivatives of q_i and p_i to
partial derivatives of the Hamiltonian function H(q, p, t), creating a
system of first-order differential equations, in contrast to the second-
order Lagrangian formulation.
3. A monochromatic electromagnetic plane wave propagates in
vacuum. What is the phase relationship between its oscillating electric
field vector and magnetic field vector?
A) 180 degrees out of phase
B) 90 degrees out of phase with the electric field leading
C) They are in phase
D) 90 degrees out of phase with the magnetic field leading
Answer: C
Explanation: For a plane wave in vacuum, the electric and magnetic
fields oscillate in phase. Maxwell's equations relate the spatial
derivative of E to the time derivative of B, leading to solutions where E
and B are proportional to the same sinusoidal function, reaching their
maximum and minimum values simultaneously.
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4. In quantum mechanics, which physical observable corresponds to the
operator -iħ(d/dx)?
A) Kinetic energy
B) Position
C) Linear momentum
D) Total energy
Answer: C
Explanation: In the position representation, the momentum operator
along the x-direction is represented by -iħ(∂/∂x), where ħ is the
reduced Planck constant. This Hermitian operator acts on the
wavefunction, and its eigenvalues correspond to the momentum values
of a particle.
5. A thermodynamic process that occurs without any heat transfer
between the system and its surroundings is termed:
A) Isothermal
B) Isobaric
C) Isochoric
D) Adiabatic
Answer: D
Explanation: An adiabatic process is defined by the condition Q = 0.
According to the first law of thermodynamics, the change in internal
energy equals the work done on the system. Temperature, pressure,
, 4|Page
and volume can all change in an adiabatic process, unlike in isothermal,
isobaric, or isochoric processes, respectively.
6. A particle with mass m is confined in a one-dimensional infinite
potential well of width L. How does the energy difference between the
first excited state and the ground state scale with L?
A) Proportional to L
B) Proportional to L^2
C) Proportional to 1/L
D) Proportional to 1/L^2
Answer: D
Explanation: The energy eigenvalues for a particle in an infinite well are
E_n = (n^2 π^2 ħ^2)/(2mL^2). The ground state (n=1) and first excited
state (n=2) give an energy difference ΔE = E_2 - E_1 = (3π^2
ħ^2)/(2mL^2), which is inversely proportional to the square of the well
width, L^2.
7. What is the fundamental postulate of special relativity regarding the
speed of light in vacuum?
A) It depends on the motion of the source
B) It depends on the motion of the observer
C) It is the same for all inertial observers
D) It is infinite in the absence of mass
Answer: C
GT Students Final Quiz 2026-2027 BANK QUESTIONS WITH
DETAILED VERIFIED ANSWERS EXAM QUESTIONS WILL
COME FROM HERE (100% CORRECT ANSWERS A+ GRADED
1. In classical mechanics, if the net external force acting on a system of
particles is zero, which of the following quantities is necessarily
conserved?
A) Kinetic energy
B) Potential energy
C) Linear momentum
D) Angular momentum about an arbitrary point
Answer: C
Explanation: According to Newton's second law for a system of
particles, the net external force equals the time rate of change of total
linear momentum. If the net external force is zero, the derivative is
zero, implying that the total linear momentum vector is constant.
Kinetic energy may not be conserved if internal forces do work, and
angular momentum conservation requires zero net external torque, not
just zero force.
2. The Hamiltonian formulation of mechanics elegantly expresses the
equations of motion in terms of which two fundamental quantities?
,2|Page
A) Generalized coordinates and velocities
B) Generalized coordinates and conjugate momenta
C) Time and action
D) Position and acceleration
Answer: B
Explanation: In Hamiltonian mechanics, the state of a system is
described by generalized coordinates q_i and their conjugate momenta
p_i. Hamilton's equations relate the time derivatives of q_i and p_i to
partial derivatives of the Hamiltonian function H(q, p, t), creating a
system of first-order differential equations, in contrast to the second-
order Lagrangian formulation.
3. A monochromatic electromagnetic plane wave propagates in
vacuum. What is the phase relationship between its oscillating electric
field vector and magnetic field vector?
A) 180 degrees out of phase
B) 90 degrees out of phase with the electric field leading
C) They are in phase
D) 90 degrees out of phase with the magnetic field leading
Answer: C
Explanation: For a plane wave in vacuum, the electric and magnetic
fields oscillate in phase. Maxwell's equations relate the spatial
derivative of E to the time derivative of B, leading to solutions where E
and B are proportional to the same sinusoidal function, reaching their
maximum and minimum values simultaneously.
,3|Page
4. In quantum mechanics, which physical observable corresponds to the
operator -iħ(d/dx)?
A) Kinetic energy
B) Position
C) Linear momentum
D) Total energy
Answer: C
Explanation: In the position representation, the momentum operator
along the x-direction is represented by -iħ(∂/∂x), where ħ is the
reduced Planck constant. This Hermitian operator acts on the
wavefunction, and its eigenvalues correspond to the momentum values
of a particle.
5. A thermodynamic process that occurs without any heat transfer
between the system and its surroundings is termed:
A) Isothermal
B) Isobaric
C) Isochoric
D) Adiabatic
Answer: D
Explanation: An adiabatic process is defined by the condition Q = 0.
According to the first law of thermodynamics, the change in internal
energy equals the work done on the system. Temperature, pressure,
, 4|Page
and volume can all change in an adiabatic process, unlike in isothermal,
isobaric, or isochoric processes, respectively.
6. A particle with mass m is confined in a one-dimensional infinite
potential well of width L. How does the energy difference between the
first excited state and the ground state scale with L?
A) Proportional to L
B) Proportional to L^2
C) Proportional to 1/L
D) Proportional to 1/L^2
Answer: D
Explanation: The energy eigenvalues for a particle in an infinite well are
E_n = (n^2 π^2 ħ^2)/(2mL^2). The ground state (n=1) and first excited
state (n=2) give an energy difference ΔE = E_2 - E_1 = (3π^2
ħ^2)/(2mL^2), which is inversely proportional to the square of the well
width, L^2.
7. What is the fundamental postulate of special relativity regarding the
speed of light in vacuum?
A) It depends on the motion of the source
B) It depends on the motion of the observer
C) It is the same for all inertial observers
D) It is infinite in the absence of mass
Answer: C
