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1. The Hamilton’s principle,

 States that the path actually traversed by a conservative Holonomic dynamic system from time t1 to time t2 is [ ]

 
 
 
 

2. For a conservative system where the coordinate transformations is independent of time, the Hamiltonian function (H) represents [ ]

 
 
 
 

3. The Lagrange’s equation for a conservative system is ________ [ ]

 

 
 
 
 

4. The canonical transformation

 represent [ ]

 
 
 
 

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

 
 
 
 

6. A conservative system takes a path that the integral 1∫² Pi q’j dt

 

 
 
 
 

7. For a free particle the principle of least action is

D) None

 
 
 
 

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

 
 
 
 

9. 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.

 
 
 
 

10. 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 [ ]

 
 
 
 

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

 
 
 
 

12. 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

 

 
 
 
 

13. The condition for holonomic constraint is

                 

                

 
 
 
 

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

 
 
 
 

15. Lagrangian formalism transformation to Hamiltonian formalism meant [ ]

 
 
 
 

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

 
 
 
 

17. Lagrangian for a compound pendulum is ________ [ ]

               

 
 
 
 

18. The correct relations for Poisson brackets are : [ ]

                      

                                   

 
 
 
 

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

 
 
 
 

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

 
 
 
 

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

 
 
 
 

22. The relation between Poisson and Lagrange’s brackets is

d) None of these

 
 
 
 

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

 
 
 
 

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

 
 
 
 

25. A configuration space is a space of [ ]

(l → constraints)

 
 
 
 

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

 
 
 
 

27. For a charged particle in an electromagnetic field, the Hamiltonian H is represented as ______ [ ]

                      

                              

 
 
 
 

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

 
 
 
 

Question 1 of 28

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