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1. In case of modified Hamilton’s principle, [ ]

a) the path refers to configuration space.          b) the path refers to phase space

0

2. Reduced mass of hydrogen atom is nearly equal to [ ]

3. If a system of free particles is in equilibrium, then the total work done by all forces internal and external in a virtual displacement is [ ]

4. Which of the following is invariant under Galilean transformation equations : [ ]

5. Equation of motion for bead sliding on a uniformly rotating wire in a force free space is _

a) r´ = rω²                                    b) θ’ + mglθ/I = 0

c) 2mrr’θ’ + mr²θ = 0              d) θ’ + θg/l = 0

6. The number of degrees of freedom for a system of N particles subject to k independent constraints, will be [ ]

7. Generalized momentum p_k corresponding to the generalized co – ordinate q_k is defined as

a)   ∂L /∂q_k
b)   ∂L /∂q’_k

c)  d(∂L /∂q_k)/dt

d) none of these

8. Hamiltonian is conserved only when it [ ]

9. Choose the correct statement / statements : [ ]

a) The generating function  generates the identity transformation
b) The generating function  cannot generates the identity transformation
c) The generating function F = -∑_kP_kq_k generates the identity transformation
d) None

10. If a co-ordinate corresponding to a rotation is cyclic, rotation of the system about given axis remains invariant then the following quantity is conserved ______ [ ]

11. The generalized momentum p_x of a particle of mass m with velocity v_x in an electromagnetic field is given by [ ]

a) p_x = m v_x                                             b) p_x = m v_x + qA_x

c) p_x = m v_x – qA_x                                       d) p_x = qv_xA_x

12. If the Lagrangian does not depend on time explicitly, [ ]

13. In a non – inertial frame of reference, a body experiences Coriolis force only when :

14. A physical system is invariant under rotation about a fixed axis. Then the following quantity is conserved _____ [ ]

15. Law of conservation of energy is a consequence of [ ]

16. If a co-ordinate is cyclic, Hamiltonian would reduce the number of variables in new formulation by ________ [ ]

17. The operator which represents the two variables should commute if the Poisson bracket of two variables have value ______ [ ]

18. Whenever the Lagrangian for a system does not contain a coordinate explicitly [ ]

a) q_k and p_k are cyclic coordinate
b) p_k is cyclic coordinate

c) p_k the generalized momentum, is a constant of motion.
d) q_k is always zero

19. Jocobi identity for Poisson bracket ____ [ ]

20. In case of canonical transformations [ ]

21. Homogentity of time leads to conservation of [ ]

22. Angular momentum is conserved if the system is [ ]

23. Poisson brackets for angular momentum components ((J_x ,J_y ,J_z ) does not satisfy the relation [ ]

a) [J_x ,p_x ] = 0                          b) [J_x ,p_z ] = -p_y

c) [J_y ,J_z ] = J_x                             d) [J_y ,J_z ] = -J_x

24. The generalised momentum is given by [ ]

a)  ∂T/∂q’_k                                  b) ∂T/∂q_k

c) ∂L/∂q_k                                     d) ∂L/∂q’_k

25. Expression for generalized force Q_j is

d) none of these

26. Product of any generalized momentum all the associated (also known as conjugate) coordinate must always have the dimensions of [ ]

27. For an electric circuit comprising an inductance L and capacitance C, charged to q coulombs and the current flowing in the circuit is i amperes, Lagrangian can be represented as ____ [ ]

a) L q’² – q²/C

b) 1/2 Lq² – 1/2 *q²C

c) 1/2 Lq² – 1/2 *(q²/C)

d)1/2 Lq² + 1/2 *(q²/C)

28. Which of the following is incorrect ?