M.Sc. (Semester (CBCS) Examination Mar/Apr-2018
Physics (Materials Science)
CLASSICAL MECHANICS
Time: 2½ Hours
Max. Marks: 70
Instructions: Attempt in all five questions. Q.1 and Q.2 are compulsory. Attempt any three questions from Q. 3 to 7. Figures to the right indicate full marks.
Q.1

Choose the correct alternative:
08
The Lagrangian of the system gives of the system.
difference in kinetic and potential energy
addition of kinetic and potential energy
power
rate of change of energy
Which of the following physical quantity is conserved if total external torque acting on system of particles is zero?
Linear momentum
Angular momentum
Kinetic energy
Potential energy
Atwood‟s machine is example of constraint.
holonomic and scaleronomous
non-holonomic
non-holonomic and rheonomous
rhenomous
According to Hamiloton‟s principle, the action integral for monogenic, conservative system should produce value.
unit
zero
maximum
extremum
In Euler-Lagrange‟s equation the term, dimensionally represents.
generalized force
generalized momentum
energy
nothing
In central force problem, conservation of both and takes place.
energy, angular momentum
energy, torque
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 to be valid in non-inertial frame, one requires
psudo force
real force
central force
conservative force
Page 2 of 2
SLR-UN-473

State whether the following statement is True or False:
06
Lagrange‟s approach cannot be treated as an alternative to Newtonian approach.
In case of conservative force, work done between two points is dependent on the path taken between those two points.
For "actual path" action integral gives extremum value that is maximum value.
Generalized co-ordinates need not be necessarily orthogonal curvilinear co-ordinates.
Form of the Hamilton‟s equations of motion remains invariant under canonical transformation.
In canonical transformation, new set of co-ordinates are cyclic.
Q.2
Write a short note on:
Conservation laws in central force motion
05
Principle of least action
05
Any two conservation laws for system of particles
04
Q.3
Attempt the following questions:
Starting with D „Almbert‟s principle, derive Euler-Lagrange‟s equation.
08
Set up an equation of motion for Atwood‟s machine using Euler-Lagrange‟s equation.
06
Q.4
Attempt the following questions:
Starting from Hamilton‟s principle, obtain Euler-Lagrange equation.
08
Set up Hamiltonian for simple pendulum and derive equation of motion for it using the same Hamiltonian.
06
Q.5
Attempt the following questions:
Discuss in detail four standard forms of canonical transformations.
08
Show that the transformation is canonical.
06
Q.6
Write a short note on:
In case of central force motion set up differential equation for orbit and hence deduce law of conservation of angular momentum for it
08
In central force motion, discuss the motion under different cases of force constant in inverse square law.
06
Q.7
Write a short note on:
Derive Hamilton‟s canonical equation of motion in terms of Poisson bracket.
08
Define Poisson bracket and give its any four important properties.
06