GATE PH purpose:exam-prep PYQs & Answers — Page 44

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Questions 431–440 of 650. Imported answers require independent review unless marked reviewed.

Topic practice 650 questionsPage 44 of 65

Consider the Lagrangian

, where

and

are constants. If

and

are the momenta conjugate to the coordinates

and

respectively, then the Hamiltonian is

Your answerChoose one option.

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Which one of the following matrices does NOT represent a proper rotation in a plane?

Your answerChoose one option.

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A uniform magnetic field

exists in an inertial frame

. A perfect conducting sphere moves with a constant velocity

with respect to this inertial frame. The rest frame of the sphere is

(see figure). The electric and magnetic fields in

and

are related as

The induced surface charge density on the sphere (to the lowest order in

) in the frame

Your answerChoose one option.

maximum along

uniform over the sphere

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A charge

moving with uniform speed enters a cylindrical region in free space at

and exits the region at

(see figure). Which one of the following options best describes the time dependence of the total electric flux

, through the entire surface of the cylinder?

Your answerChoose one option.

Diagram for Physics question 34 (figure 2)

Diagram for Physics question 34 (figure 3)

Diagram for Physics question 34 (figure 4)

Diagram for Physics question 34 (figure 5)

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Consider a one-dimensional non-magnetic crystal with one atom per unit cell. Assume that the valence electrons (i) do not interact with each other and (ii) interact weakly with the ions. If

is the number of valence electrons per unit cell, then at 0 K,

Your answerChoose one option.

the crystal is metallic for any value of

the crystal is non-metallic for any value of

the crystal is metallic for even values of

the crystal is metallic for odd values of

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According to the Fermi gas model of the nucleus, the nucleons move in a spherical volume of radius

, where

is the mass number and

is an empirical constant with the dimensions of length. The Fermi energy of the nucleus

is proportional to

Your answerChoose one option.

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Consider a two dimensional crystal with 3 atoms in the basis. The number of allowed optical branches (

) and acoustic branches (

) due to the lattice vibrations are

Your answerChoose one option.

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The internal energy

of a system is given by

, where

is a constant of appropriate dimensions;

and

denote the volume and entropy, respectively. Which of the following gives the correct equation of state of the system?

Your answerChoose one option.

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The potential energy of a particle of mass

is given by

The angular frequency of small oscillations of the particle about

Your answerChoose one option.

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The radial wave function of a particle in a central potential is given by

, where

is the normalization constant and

is positive constant of suitable dimensions. If

is the most probable distance of the particle from the force center, the value of

is _____.

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GATE PH purpose:exam-prep PYQs

Question 31

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Question 34

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Question 36

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Question 40