CLASSICAL MECHANICS (PREVIOUS SET QUESTIONS)

  Module 2. Classical Mechanics

 Newton’s laws, Dynamical systems, Phase space dynamics, stability analysis. Central force motions. Two body Collisionsscattering in laboratory and Centre of mass frames. Rigid body dynamics – moment of inertia tensor. Non–inertial frames and pseudoforces. Variational principle. Generalized coordinates. Lagrangian and Hamiltonian formalism and equations of motion. Conservation laws and cyclic coordinates. Periodic motion: small oscillations, normal modes. Special theory of relativity- Lorentz transformations, relativistic kinematics and mass-energy equivalence, Poisson brackets and canonical transformations. Hamiltonian-Jacobi theoryPRE

PREVIOUS YEAR QUESTION PAPER

SET 2019/7

1.Dimension of Lagrangian is -------.

A) MLT ^ -1    B) MLT^-2 C) ML^2T^-1   D) ML^2T^-2 

18. Which among the following is true for constraints

A) holonomic constraint can be expressed as an algebraic equation

B) non-holonomic constraint can be expressed as a differential equation

C) Constraint force corresponding to rheonomous constraints cannot do work

D) A constraint can be holonomic and scleronomous at the same time

19. Hamilton’s principle is defined in --------.

A) configuration space          B) phase space       C) eucledian space             D) none of these

20. Which among the following is NOT TRUE?

A) Generalized coordinates can have any dimension

B) Generalized momenta should always have the dimension of angular momentum

C) Lagrangian is defined in terms of generalized coordinates, generalized velocities

and time.

D) Hamiltonian and Lagrangian are related through Legendre transformation

21. Law of conservation of angular momentum is a consequence of ---------.

A) Homogeneity of space

B) Isotropy of space

C) Homogeneity of flow of time

D) Law of conservation of energy

22. Hamilton-Jacobi method is used for solving --------systems.

A) conservative         B) nonconservative         C) holonomic          D) periodic

23. For a particle moving under central force, -------is conserved.

A) linear momentum       B) kinetic energy      C) angular momentum          D) potential energy

28. Number of degrees of freedom for a mass point constrained move along the circumference

of a circle = -------.

A) 1     B) 2      C) 3       D) 0

39. A rod of proper length 1 metre long is moving along its length. For an observer in earth the

length of the rod is 0.8 m. The velocity of the rod with respect to earth is -------; c is the

speed of light.

A) c B) 0.8c C) 0.66c D) none of these

40. Meson paradox can be explained using -------.

A) length contraction                                        B) time dilation

C) both length contraction and time dilation     D) none of these

41. An α-particle is moving with a speed of 0.7 c in a direction opposite to the direction of a

moving photon. The relative velocity of the photon with respect to the α-particle is ------

A) 1.7c         B) c             C) 0.7c           D) 0.3c

44. Which among the following is TRUE?

A) Constancy of speed of light is consistent with Galilean transformations

B) Constancy of speed of light is not consistent with Fourier transformations

C) Constancy of speed of light is not consistent with Galilean transformations

D) Constancy of speed of light is consistent with Fourier transformations.

SET 2019/2

91. The Lagrangian of a mechanical system with two degree of freedom x and y is

L = (x')^2 + (Y')2. The Hamiltonian of the system is

A)(1/4)*[Px^2+Py^2]

92. 2 bodies of masses m and 2m are connected by a massless spring of constant k. If 'w'(omega)

is the angular frequency of oscillations, then w^2 =

C)(3K)/(2m)