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

1. Match the following [ ]

Cases                                                                                 Degrees of freedom

(i) Rigid body moving in free space                                             (A) 5

(ii) Bob of a simple pendulum oscillating in a plane                (B) 6

(iii)Dumbell moving in space                                                        (C) 1

2. The correct relations for Poisson brackets are : [ ]    3. For a conservative system where the coordinate transformations is independent of time, the Hamiltonian function (H) represents [ ]

4. Lagrangian for a compound pendulum is ________ [ ]    5. A conservative system takes a path that the integral 1∫² Pi q’j dt

6. Lagrange’s equations of motion are second order equations, the degrees of freedom for this are _________ [ ]

7. The condition for holonomic constraint is    8. A configuration space is a space of [ ]

(l → constraints)

9. If Φ’ changes its sign between the limiting values of θ then the possible motion of heavy symmetric top is [ ]

10. The action integral of a physical system for the actual path is [ ]

11. The Lagrange’s equation of motion is a differential equation of [ ]

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

13. If all forces in a system are derived from a generalized potential then it is called a

14. If Pk and qk (k = 1, 2, 3) represent the momentum and position coordinates respectively for a particle, [ ]

15. A small marble rolling on a rough surface without slipping is an example [ ]

16. If ∂L/∂q = 0, where L is the Lagrangian for a conservative system without constraints and q is a generalized coordinate, then the generalized momentum is [ ]

17. The relation between Poisson and Lagrange’s brackets is   d) None of these

18. Which of the following constraint contains time explicitly ? [ ]

19. For a charged particle in an electromagnetic field, the Hamiltonian H is represented as ______ [ ]    20. The canonical transformation represent [ ]

21. About the principal axes the number of non – zero elements of inertia tensor will be

22. The Hamilton’s principle, States that the path actually traversed by a conservative Holonomic dynamic system from time t1 to time t2 is [ ]

23. The principle of virtual work asserts that the system of particles will be in equilibrium only if

24. Law of conservation of angular momentum is a consequence of [ ]

25. Lagrangian formalism transformation to Hamiltonian formalism meant [ ]

26. Lagrangian of the Sun – Earth System is [ ]    Here is the Sun – Earth distance, M and m are the masses of the Sun and Earth respectively.
θ is the angular speed, and G the gravitational constant.

27. The Lagrange’s equation for a conservative system is ________ [ ]    28. For a free particle the principle of least action is   D) None

Question 1 of 28