CSIR (Council of Scientific & Industrial Research) Physical Sciences: Questions 212 - 214 of 463

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Question number: 212

» Classical Mechanics » Lagrangian and Hamiltonian Formalism and Equations of Motion

Appeared in Year: 2013

MCQ▾

Question

A system is governed by Hamiltonian,

Equation

Where a and b are constant are Equation are momenta conjugate to Equation and Equation respectively. For what value of Equation and Equation will the quantities Equation and Equation be conserved? (June)

Choices

Choice (4) Response

a.

Equation

b.

Equation

c.

Equation

d.

Equation

Question number: 213

» Mathematical Methods of Physics » Poles, Residues & Evaluation of Integrals

Appeared in Year: 2012

MCQ▾

Question

The value of the integral Equation , where C is a closed contour defined by the equation Equation , traversed in the anti – clockwise direction, is –

(December)

Choices

Choice (4) Response

a.

Equation

b.

Equation

c.

Equation

d.

Equation

Question number: 214

» Classical Mechanics » Phase Space Dynamics

MCQ▾

Question

Which of the following set of phase – space trajectories is not possible for a particle obeying Hamilton’s equations of motion? (December)

Choices

Choice (4) Response

a.

A phase – space trajectories – Choice A

A Phase – Space Trajectories – Choice a

In figure a phase – space trajectories is shown.

b.

A phase – space trajectories – Choice B

A Phase – Space Trajectories – Choice B

In figure a phase – space trajectories is shown.

c.

A phase – space trajectories – Choice C

A Phase – Space Trajectories – Choice C

In figure a phase – space trajectories is shown.

d.

A phase – space trajectories – Choice D

A Phase – Space Trajectories – Choice D

In figure a phase – space trajectories is shown.

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