Posted on : May 22, 2019 By myeduhub Online Exams Physics (level PG) Please enter your email: 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) a b c d 2. Jocobi identity for Poisson bracket ____ [ ] a) [X, [Y, H]] + [Y, [H, X]] + [H, [X, Y]] = 0 b) [X, [Y, H]] – [Y, [H, X]] + [H, [X, Y]] = 0 c) [X, [Y, H]] + [Y, [H, X]] – [H, [X, Y]] = 0 d) [X, [Y, H]] – [Y, [H, X]] – [H, [X, Y]] = 0 3. In case of modified Hamilton’s principle, [ ] a) the path refers to configuration space. b) the path refers to phase space 0 a b c d 4. Hamiltonian is conserved only when it [ ] a) explicitly depends on time b) implicitly depends on time c) independent of time d) always H is conserved 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 a b c d 6. The generalised momentum is given by [ ] a) ∂T/∂q’k b) ∂T/∂qk c) ∂L/∂qk d) ∂L/∂q’k a b c d 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 a b c d 8. The number of degrees of freedom for a system of N particles subject to k independent constraints, will be [ ] a) 3N – k b) 3N + k c) 3 N d) none of these 9. A physical system is invariant under rotation about a fixed axis. Then the following quantity is conserved _____ [ ] a) Total linear momentum b) Linear momentum along the axis of rotation c) Total angular momentum d) Angular momentum along the axis of rotation 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 a b c d 11. If the Lagrangian does not depend on time explicitly, [ ] a) the Hamiltonian is constant b) the Hamiltonian cannot be constant. c) the kinetic energy is constant. d) the potential energy is constant. 12. Law of conservation of energy is a consequence of [ ] a) homogeneity of space b) homogenetity of time c) isotropy of space d) homogeneity of space and time 13. Product of any generalized momentum all the associated (also known as conjugate) coordinate must always have the dimensions of [ ] a) linear momentum b) angular momentum c) energy d) none of these 14. Which of the following is invariant under Galilean transformation equations : [ ] a) space co-ordinates b) velocity c) momentum d) force 15. Homogentity of time leads to conservation of [ ] a) linear momentum b) angular momentum c) total energy d) kinetic energy 16. In case of canonical transformations [ ] a) The form of the Hamilton’s equations is preserved b) The form of the Hamilton’s equations can not be preserved. c) The form of the Hamilton’s equations may or may not be preserved. d) None 17. Angular momentum is conserved if the system is [ ] a) symmetric under rotation b) asymmetric under rotation c) symmetric under translation d) asymmetric under translation 18. In a non – inertial frame of reference, a body experiences Coriolis force only when : a) the frame has rotational motion and the body also rotates b) the frame has rotational motion and body is at rest c) the frame has rotational motion and body has linear motion d) none of the above 19. The operator which represents the two variables should commute if the Poisson bracket of two variables have value ______ [ ] a) 1 b) 0 c) ih/2Π d) −ih/2Π 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 ______ [ ] a) Linear momentum b) Angular momentum c) Kinetic energy d) Potential energy 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 a b c d 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 a b c d 23. Which of the following is incorrect ? a) Central forces are long range forces b) Work done by a central force over a closed path is always zero c) Central forces can be derived from the corresponding scalar potential d) Nuclear force is a central force 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 a b c d 25. If a co-ordinate is cyclic, Hamiltonian would reduce the number of variables in new formulation by ________ [ ] a) One b) Two c) Three d) Four 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 [ ] a) zero b) positive c) negative d) none of these 27. Reduced mass of hydrogen atom is nearly equal to [ ] a) mass of a proton b) mass of electron c) sum of masses of proton and electron d) difference of masses of proton and electron 28. Expression for generalized force Qj is d) none of these a b c d Loading … Question 1 of 28
