TEST 6

PPSC PHYSICS
CLASSICAL MECHANICS + STATISTICAL PHYSICS
1) As there are three generalized coordinates, then Hamilton’s canonical equations will
be … in number
(a) Three (b) Four (c) Five (d) Six
2) If the Poisson bracket of a function with the Hamiltonian vanishes6
(a) the function depends upon time
(b) the function is a constant of motion
(c) the function is not the constant of motion
(d) None of these
3) Hamiltonian H is defined as
(a) the total energy of the system (b) the difference in energy of the system
(c) the product of energy of the system (d) All of these
4) Whenever the Lagrangian for a system does not contain a coordinate explicitly,
(a) pk is cyclic coordinate
(b) pk the generalized momentum, is a constant of motion
(c) qk is always zero
(d) None of these
5) The dimensions of generalized momentum
(a) are always those of linear momentum (b) may be those of angular momentum
(c) may be those of linear momentum (d) Both B and C are true
6) The Lagrangian equation of motion are……order differential equations.
(a) first (b) second (c) third (d) forth
7) Poisson bracket is useful to find the
(a) Integrals of motion
(b) Equations of motion
(c) Lagrange function
(d) Hamilton’s function
8) If the coordinates (Q,P) satisfy the canonical Poisson bracket ------------ , then the
transformation (q , p)→(Q,P) is canonical if
(a) [Q,Q]=0
(b) [P,P]=0
(c) [Q,P]=1
(d) None of these
(e) All of these
9) The statement “If F(q, p, t) and G (q, p, t) are two integrals of motion. then [F, G] is
also an
integral of motion” is called
(a) Legendre’s transformations
(b) Jacobi-Poisson’s theorem
(c) Hamilton’s principle
(d) None of these
10) Dimension of space defined in ( pi ,qi ,t ) is
(a) 2n
(b) 2n+1
(c) 4n
(d) 4n+1
11) Which one is correct
(a) The Poisson brackets do not give a complete solution of a system of motion
but are very helpful in finding the Integrals of motion
(b) The Poisson brackets give a complete solution of a system of motion and are very
helpful in finding the Integrals of motion.
(c) The Poisson brackets do not give a complete solution of a system of motion and do
not helpful in finding the Integrals of motion.
(d) The Poisson brackets give a complete solution of a system of motion but do not
helpful in finding the Integrals of motion.
12) The transformation of canonical coordinates (q, p) to (Q, P) preserving the form
of Hamilton’s equations is called ______.
(a)Hamilton transformation (b)Canonical transformation
 (c)Preserved transformation (d) Point transformation
13) Hamilton’s principle is an example of a:
(a) Force (b) Lagrange multiplier
(c) stationary point (d) variational principle.
14) The Hamiltonian can be constructed from the Lagrangian using the formula:
(a) H = ˙piq˙i – L (b) H = piqi – L (c) H = ∂L/∂q˙i (d) H =1/L
15) Hamiltonian formulation is an alternative formulation of advanced classical
mechanics that is -------- to the Lagrangian formulation.
(a) Inferior in some respects (b) superior in some respects
(c) equal in all aspects (d) None
16) The transformation of Lagrangian to Hamiltonian is done by:
(a) Legendre transformation (b) Lorentz transformation
(c) Galilean transformation (d) None
17) A force “F” is conservative if
a) ∇×F≠ 0 b) 𝛁×F=0 c) ∇.F ≠0 d) ∇.F=0
18) When a planet orbits the Sun, one of the foci of the elliptical orbit is
a. The axis
b. The perihelion
c. The Centre
d. The Sun
19) In the elliptical orbit the speed of satellite minimum at
a. Apogee
b. Perigee
c. Same everywhere
d. Foci
20) The statement ‘For a conservative holonomic system, the line integral of
Lagrangian function from initial time to final time has an extreme value” describes?
(a) D’ Alembert principle (b) Hamilton’s principle
(c) Poisson’s theorem (d) Modified
21) The distribution of particles at different energy levels as a function of
temperature is given by
a) Newton’s law
b) Faraday's law
c) Maxwell-Boltzmann statistics
d) Planck’s law
22) What type of system energy is related to the molecular structure of a
system?
A. Macroscopic form of energy
B. Internal energy
C. Microscopic form of energy
D. External energy
23) What is a process during which the specific volume remains constant?
A. Isobaric process
B. Isothermal process
C. Isochoric or isometric process
D. Isovolumetric process
24) How many independent properties are required to completely fix the
equilibrium state of a gaseous compound state?
A. 4
B. 3
C. 2
D. Infinite
25) Fermions obey:
A. Hund’s rule
 B. Fermi-Dirac statistics
C. Bose-Einstein’s statistics
D. Maxwell-Boltzmann’s statistics
26) Bosons obey:
A. Hund’s rule
B. Fermi-Dirac statistics
C. Bose-Einstein’s statistics
D. Maxwell-Boltzmann’s statistics
27) Which of the following is not a state function?
A. Internal energy
B. Gibb’s free energy
C. Helmholtz’s function
D. Work
28) The entropy (heat per unit temperature) is the measure of irreversibility, of
chaos, of disorder – quantitatively measured as “number of configurations”: S = kB ln
Ω
A. True
B. False
C. True for canonical ensembles
D. False for micro-canonical ensembles
29) In statistical mechanics, an ensemble is an idealization consisting of a large
number of virtual copies of a system, considered all at once, each of which represents
a possible state that the real system might be in.
A. True
B. False
C. True for closed systems
D. False for open systems
30) In statistical mechanics, the microcanonical ensemble is a statistical ensemble
that represents the possible states of a mechanical system whose total energy
is exactly specified.
A. Micro-canonical ensemble
B. Canonical ensemble
C. Energy ensemble
D. Conservative ensemble
31) The statistical ensemble that represents the possible states of a mechanical
system in thermal equilibrium with a heat bath at a fixed temperature. The
system can exchange energy with the heat bath, so that the states of the system will
differ in total energy.
A. Micro-canonical ensemble
B. Canonical ensemble
C. Energy ensemble
D. Conservative ensemble
32) One particle can only occupy one quantum state at a time.
A. Bosons
B. Fermions
 C. Baryons
D. Hyperons
33) All bosons have either zero spin or an even integer spin.
A. True
B. False
C. True for bound systems
D. False for free systems
34) According to Debye model, at high temperature, the internal energy can be
expressed as:
A. 3NkBT
B. (3N-1)kBT
C. NkBT
D. (3N)2 kBT
35) A photon gas in thermal equilibrium at temperature T with a system has energy
emitted per unit time per unit area proportional to
A. T4
B. T2
C. T3
D. √𝑇
36) According to Fermi distribution, the probability of being at Fermi energy level is:
A. 0.5
B. 1
C. 0.75
D. 0
37) Fermi particles must occupy increasingly high levels of energy but Bose particles
should not do the same.
A. Pauli’s principle
B. Hund’s rule
C. Gibb’s ensemble law
D. Stefan’s law
38) For increasing heat absorption in an ensemble, the number of possible energy
states .
A. Always increase
B. Always decrease
C. Does not change
D. Decreases to zero
39) Everything about the system can be found by calculating:
A. Partition function
B. Distribution function
C. Incremental function
D. Gibb’s function