CSIR Physical Sciences: Questions 253 - 255 of 401

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Question number: 253

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

Appeared in Year: 2012

MCQ▾

Question

The Hamiltonian of a simple pendulum consisting of a mass m attached to a massless string of length l is H=pθ22ml2+mgl(1cosθ) . If L denotes the Lagrangian, the value of dLdt is – (December)

Choices

Choice (4) Response

a.

glpθcosθ

b.

2glpθsinθ

c.

glpθsin2θ

d.

lpθ2cosθ

Question number: 254

» Mathematical Methods of Physics » Matrices

Appeared in Year: 2012

MCQ▾

Question

Given a 2×2 unitary matrix U satisfying U+U=UU+=1 with detU=eiφ , one can construct a unitary matrix V(V+V=VV+=1) with detV=1 from it by, (December)

Choices

Choice (4) Response

a.

Multiplying U by eiφ

b.

Multiplying U by eiφ2

c.

Multiplying any single element of U by eiφ

d.

Multiplying any row or column of U by eiφ2

Question number: 255

» Quantum Mechanics » Elementary Theory of Scattering » Born Approximation

Appeared in Year: 2014

MCQ▾

Question

The scattering amplitude f(θ) for the potential V(r)=βeμr ; where β and μ are positive constants, is given, in the Born approximation, by (in the following b=2ksinθ2 and E=2k22m ) – (June – 2014)

Choices

Choice (4) Response

a.

4mβμ2b2(b2+μ2)

b.

4mβμ2(b2+μ2)2

c.

4mβμ2b2+μ2

d.

4mβμ2(b2+μ2)3

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