• ## NASA’s Exoplanet Mission Finds 1st Earth Size Alien World

1. 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)

2. Jocobi identity for Poisson bracket ____ [ ]

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

a) the path refers to configuration space.          b) the path refers to phase space  0

4. Hamiltonian is conserved only when it [ ]

5. Generalized momentum pk corresponding to the generalized co – ordinate qk is defined as

a)   ∂L /∂qk
b)   ∂L /∂q’k

c)  d(∂L /∂qk)/dt

d) none of these

6. The generalised momentum is given by [ ]

a)  ∂T/∂q’k                                  b) ∂T/∂qk

c) ∂L/∂qk                                     d) ∂L/∂q’k

7. 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

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

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

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

a) qk and pk are cyclic coordinate
b) pk is cyclic coordinate

c) pk the generalized momentum, is a constant of motion.
d) qk is always zero

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

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

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

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

15. Homogentity of time leads to conservation of [ ]

16. In case of canonical transformations [ ]

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

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

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

20. 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 ______ [ ]

21. Poisson brackets for angular momentum components ((Jx ,Jy ,Jz ) does not satisfy the relation [ ]

a) [Jx ,px ] = 0                          b) [Jx ,pz ] = -py

c) [Jy ,Jz ] = Jx                             d) [Jy ,Jz ] = -Jx

22. 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 = -∑kPkqk generates the identity transformation
d) None

23. Which of the following is incorrect ?

24. The generalized momentum px of a particle of mass m with velocity vx in an electromagnetic field is given by [ ]

a) px = m vx                                             b) px = m vx + qAx

c) px = m vx – qAx                                       d) px = qvxAx

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

26. 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 [ ]

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

28. Expression for generalized force Qj is   d) none of these

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