M.Sc. (Physics-Material Science) (Semester
(CBCS) Examination, 2017
CLASSICAL MECHANICS
Day Date: Tuesday, 25-04-2017 Max. Marks: 70
Time: 10.30 AM to 01.00 PM
Instruction Attempt in all Five questions.
Q.NO.1 and Q.NO.2 are compulsory.
Attempt any 3 questions from Q.No.3 to Q.No.7.
Figure to the right indicates full marks.
Q.1 Choose only one correct alternatives 08
Constraint in case of simple pendulum attached to rigid support is an
example of
holonomic constraint
non-holonomic constraint
rheonomous constraint
non-holonomic and rheonomous constraint
For equilibrium of a system, the virtual work done due
applied forces is zero.
forces of constraint must be negative.
both the forces stated above must be minimum.
external forces must be strictly positive.
If Atwood's machine is kept in a ascending lift acceleration then
the common accelearation of system will be ….
The product of 'Lagrangian' for the system and has dimensions
of …..
angular momentum linear momentum
energy Impulse
According to Newton's third law, action-reaction pair …
exits simultaneously but each one of them acts on two different
objects.
acts on same object.
exits simultaneously but effective force on a object is zero.
exits at two different time instants but act on two different objects
Page 1 of 2
In harmonic oscillator, the phase difference between its position(q)
and velocity(v) is
The physical significance of "Hamilton Principle" is
nature behave economically
power consumption is conservative system is maximum.
energy consumption in conservative system is maximum.
restricted for classical system alone.
In projectile motion, under gravitational force horizontal component of
velocity ..
changes continuously. remains constant.
changes in magnitude only. Zero.
State True or False 06
Dissipation always leads to negative work.
In Euler-Lagrangian formulation of mechanism, represents a
generalized force.
Hamilton's principle is differential principle.
Cycle co-ordinates are also known as ignorable co-ordinates.
In case of conservative system, forces are derivable from a scalar
function known as potential.
Poisson's bracket always changes under canonical transformation.
Q.2 Answer the following questions.
Show that Newton's laws are invariant under Galilean transformation. 05
Discuss the motion of gyroscope. 05
Write a note on symmetries and conservation laws. 04
Q.3 Attempt the following questions.
Derive Euler-Lagrange's equation from Hamilton's principle. 10
Write a short note on Hamilton's principle. 04
Q.4 Attempt the following questions.
Obtain the solution of harmonic oscillator problem using Hamilton-Jacobi
equation.
08
Discuss the properties of Poisson's bracket. 06
Q.5 Attempt the following questions.
Derive Hamilton's canonical equation of motion 08
Reduce two-body central force problem to one-body problem. Give two
example of it.
06
Q.6 Attempt the following questions.
What are constraints? Give detailed classification of it with example of
each.
08
What are difficulties introduced by the constraints and how they are
removed?
06
Q.7 Attempt the following questions.
Show that in canonical transformation, Poisson's bracket does not vary. 08
Prove Jacobi's identity. 06