Classical Mechanics - BU 2021 Question Paper

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M.Sc. I^st Semester (New/ATKT)

Examination, 2021-22

Physics

Paper - II

Classical Mechanics

Time : 3 Hours] [Maximum Marks : 85

Note :- Attempt all the questions.

SECTION - 'A'

Objective Type Questions

1. Choose the correct answer : 10×1.5=15

(i) For Newtonian Mechanics,

(a)
\(v > c\)
(b)
\(v >> c\)
(c)
\(v = c\)
(d)
\(v < c\)

(ii) Rutherford scattering is -

(a) Elastic
(b) Inelastic
(c) Either of two about
(d) None of above

(iii) Coriolis force is an example of

(a) Inertial frame of refrence
(b) Non-inertial frame of refrence
(c) Either of two above
(d) None of above

(iv) Which of the following is lagrange's equation of motion.

(a)
\(\delta \int_{t_1}^{t_2} L dt = 0\)
(b)
\(\frac{d}{dt}\left(\frac{\partial L}{\partial \dot{q_j}}\right) - \frac{\partial L}{\partial q_j} = 0\)
(c)
\(\int_{t_1}^{t_2} (m r - F) \delta r dt = 0\)
(d) None of above

(v) D'Alembertian operator IP is invariant under -

(a) Loventz Transformation
(b) Galilean transformation
(c) Either of two above
(d) None of above

(vi) If sum of external press acting on the system of particles is zero, the total linear momentum of the system is.

(a) Unconserved
(b) Constant or conserved
(c) Neither constant nor conserved
(d) Both a and c

(vii) The limitations or geometrical restrictions on the motion of a particle or system of particles generally known as

(a) Holonomic constraints
(b) Non-Holonomic constraints
(c) Constraints
(d) None of them

(viii) If the constraints are independent of time they are fermed as.

(a) Scloronomic
(b) Rheonomic
(c) Both a and b
(d) None of them

(ix) In equilibrium, the resultant force acting on each particle of the system must be.

(a) 0
(b) 1
(c) 2
(d) 3

(x) D Alembert's principle is,

(a)
\(f_i - P_i = 0\)
(b)
\(\sum (\vec{f_i} - \vec{P_i}) \delta r_i = 0\)
(c)
\(\sum \delta r_i = 0\)
(d) None of them

SECTION - 'B'

Short Answer Type Questions

5×5=25

Note :- Short answer type 5 questions of 5 marks each with internal choice.

2. Discuss Newton's second law of motion for many particle system using ferms internal and external forces.

Explain basic conservation laws related with classical mechanics.

3. Discuss canonical transformation.

Explain principle of least action.

4. What is meant by stable and unstable equilibrium.

Discuss normal coordinates and normal modes of libration.

5. Write note on 4 momenta.

Write note on 4 force.

6. Write note on any two of the following.

(i) Configuration space
(ii) Action and angle variables
(iii) Linear bistable molecule
(iv) 4 Scalar

SECTION - 'C'

Long Answer Type Questions

9×5=45

Note :- Long answer type 5 questions of 9 mark each questions have internal choice.

7. Deduce Hamilton's principle from D'Alembert's principle.

Use lagrangian formulation for conservation of linear momentum.

8. Discuss simple algebraic properties of poisson's bracket.

Explain kepler problem.

9. Write down theory of two coupled oscillator.

Find out expression for acceleration in rotating frame of reference.

10. Write down different symmetries and associated conservation laws.

Discuss convartant four dimenstional formulation.

11. Write note on any two of the following.

(a) Equation of motion and first integral.
(b) Poisson's bracket
(c) Eigen frequency and general motion
(d) Difference between galilean and loventz transformation.