M.Sc. (Semester (CBCS) Examination Oct/Nov-2017
Physics (Materials Science)
CLASSICAL MECHANICS
Day Date: Thursday, 23-11-2017 Max. Marks: 70
Time: 10.30 AM to 01.00 PM
Instructions: Q.1 and Q.2 are compulsory.
Attempt any three questions from Q. 3 to 7.
Figures to the right indicate full marks.
Attempt in all five questions.
Q.1 Select the correct alternative: 08
The product of Lagrangian of the system and time gives in
the system.
Action Total energy
Power Linear momentum
Which of the following physical quantity is conserved if total external
force acting on system of particles is zero?
Linear momentum Angular momentum
Kinetic energy Potential energy
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,




dimensionally represents
Generalized force Generalized momentum
Energy Nothing
In central force problem conservation of and take 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 l
0 1
2 3
Newton's laws of motion are under Galilean transformation.
Invariant Variant
Changes its form Changes its sign.
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SLR-MO-516
Q.1 State whether statement is true or false:- 06
Euler-Lagrange's approach can be treated as one of the formulations in
classical mechanics as an alternative to Newtonian approach.
If the system is subjected to conservative force then work done
between two points is independent of path between those two points.
For "actual path" action integral gives extremum value that is minimum
value.
Generalized co-ordinates need to be necessarily orthogonal curvilinear
co-ordinates.
Form of the Hamilton's equations of motion remains invariant under
canonical transformation.
In canonical transformation, new set co-ordinates are not cyclic.
Q.2 Write a short note on
Conservation laws in central force motion. 05
Hamilton's principle. 05
Conservation laws for single particle. 04
Q.3 Attempt the following questions:-
Starting with Almbert's principle, derive Euler-Lagrange's equation. 08
Set up an equation of motion for one dimensional harmonic oscillator using
Euler-Lagrange's equation.
06
Q.4 Attempt the following questions:-
Deduce Euler-Lagrange equation from Hamilton's principle. 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 canonical transformations with its four standard forms. 08
Show that the transformation

2
Q=tan-1


is canonical. 06
Q.6 Write short note on
In central force motion, set up differential equation for orbit and show how it
leads to conservation of angular momentum?
08
In central force motion, discuss the motion under different cases of force
constant in inverse square law.
06
Q.7 Write 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