M.Sc. (Semester (CBCS) Examination Nov/Dec-2018
Physics (Materials Science)
CLASSICAL MECHANICS
Time: 2½ Hours Max. Marks: 70
Instructions: Attempt all the questions.
Figures to the right indicate full marks.
Q.1 Choose the correct alternative 14
The product of Lagrangian of the system and time gives in the
system.
Power Action
Total energy Linear momentum
Which of the following physical quantity is conserved if total external force
acting on system of particles is zero?
Angular momentum Kinetic energy
Potential energy Linear momentum
Condition of rigid body constraint is example of constraint.
Holonomic Non-holonomic
Non-holonomic and rheonomous Rheonomous
According to Hamiloton's principle, delta variation of action integral for
monogenic, conservative system produces value.
Unit Zero
Maximum Extremum
In Euler-Lagrange's equation,



3
dimensionally reprents.
Generalized force Generalized momentum
Energy Nothing
In central force problem conservation of and takes place.
Energy, torque Energy, angular momentum
Angular momentum, torque Linear momentum, force
In central force motion the differential equation for orbit gives absurd result for

0 1
2 3
Newton's laws of motion are under Galilean transformation.
Variant Invariant
Changes its form Changes its sign
For gauge transformation
Both the electric and magnetic field vector change.
The electric field vector changes but magnetic field vector does not change
The magnetic field vector changes but electric field vector does not change
The electric and magnetic field vector do not change
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10) Atwood's machine is example of constraint.
Holonomic and scaleronomous Non-holonomic
Non-holonomic and rheonomous Rheonomous
11) A particle is moving on elliptical path under inverse square law force of the
form the eccentricity of the orbit is
Function of total energy
Independent of total energy
Is not function of angular momentum
Independent of angular momentum
12) Rutherford differential scattering cross-section
Has dimension of area
Has dimension of length
Is proportional to the square of the kinetic energy of incident particle
Is inversely proportional to ∅ is a scattering angle
13) The phase space refers to
Position coordinate
Momentum coordinate
Both position and momentum coordinates
None of the above
14) Non-inertial frames
Are accelerated frame
Are unaccelerated frame
Are those frames in which force-free particle moves with constant velocity
None of these
Q.2 Answer the following. (Any four) 08
Starting with D'Almbert's principle derive Euler-Lagrange's equation.
Set up an equation of motion for one dimensional harmonic oscillator
using Euler-Lagrange's equation.
Define Poisson braket and give its any four important properties.
State any two conservation laws for system of particles.
What is principle of least action?
Write note on. (Any Two) 06
Rutherford Scattering
Hamilton's principle
Conservation laws for single particle
Q.3 Answer the following questions. (Any Two) 08
Deduce Euler-Lagrange equation from Hamilton's principle.
Set up Hamiltonian for simple pendulum and derive equation of motion
for it using the same Hamiltonian.
What is four standard forms of canonical transformations?
Answer the following question. (Any One) 06
In central force motion, discuss the motion under different cases of force
constant in inverse square law.
Show that the transformation

2



is canonical.
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Q.4 Answer the following questions. (Any Two) 10
Set up an equation of motion for Atwood's machine using Euler-
Lagrange's equation.
State inverse square law of force? Derive any one Kepler's law using
inverse square law.
Derive Hamiltonian-Jacobi equation.
Answer the following question. (Any One) 04
What are Galilean transformations?
Write note on gauge invariance?
Q.5 Answer the following questions. (Any Two) 14
Derive Hamilton's canonical equation of motion in terms of Poisson bracket.
In central force motion. Set up differential equation for orbit and show how it
leads to conservation of angular momentum.
Apply variational principle to show that the path of projectile is parabola.