GATE Physics: Questions 112 - 115 of 622

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Question number: 112

» Mathematical Physics » Elements of Complex Analysis » Residue Theorem and Applications

Appeared in Year: 2012

MCQ▾

Question

The value of the integral Ce1zdz , using the contour C of circle with unit radius z =1 is –

Choices

Choice (4) Response

a.

Zero

b.

2πi

c.

12πi

d.

1+2πi

Question number: 113

» Classical Mechanics » Mechanics of System of Particles

Appeared in Year: 2012

MCQ▾

Question

In a central force field, the trajectory of particle of mass m , and angular momentum L in plan polar coordinates in given by,

1r=mL2(1+εcosθ)

Where, ε is the eccentricity of the particle’s motion. Which one of the following choices for ε gives rise a parabolic trajectory?

Choices

Choice (4) Response

a.

0<ε<1

b.

ε>1

c.

ε=0

d.

ε=1

Question number: 114

» Classical Mechanics » Lagrange's and Hamilton's Formalisms

Appeared in Year: 2016

MCQ▾

Question

The Lagrangian of a system is given by

L=12ml2[θ˙+sin2θφ˙]mglcosθ , where m,landg are constants.

Which of the following is conserved?

Choices

Choice (4) Response

a.

φ˙sin2θ

b.

φ˙sin2θ

c.

φ˙sinθ

d.

φ˙sinθ

Question number: 115

» Quantum Mechanics » Linear Vectors and Operators in Hilbert Space

Appeared in Year: 2016

MCQ▾

Question

If x and p are the x components of the position and the momentum operators of a particle respectively, the commutator [x2,p2] is –

Choices

Choice (4) Response

a.

2i(xppx)

b.

i(xp+px)

c.

i(xppx)

d.

2i(xp+px)

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