GATE PH purpose:exam-prep PYQs & Answers — Page 38

Questions 371–380 of 650. Imported answers require independent review unless marked reviewed.

Consider a single one-dimensional harmonic oscillator of angular frequency

, in equilibrium at temperature

. The states of the harmonic oscillator are all non-degenerate having energy

with equal probability, where

is the quantum number. The Helmholtz free energy of the oscillator is

Your answerChoose one option.

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A system of two atoms can be in three quantum states having energies

and

. The system is in equilibrium at temperature

. Match the following Statistics with the Partition function.

Statistics	Partition function
CD: Classical (distinguishable particles)	Z1:
CI: Classical (indistinguishable particles)	Z2:
FD: Fermi-Dirac	Z3:
BE: Bose-Einstein	Z4:

Your answerChoose one option.

CD: Z1, CI: Z2, FD: Z3, BE: Z4

CD: Z2, CI: Z3, FD: Z4, BE: Z1

CD: Z3, CI: Z4, FD: Z1, BE: Z2

CD: Z4, CI: Z1, FD: Z2, BE: Z3

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The free energy of a ferromagnet is given by

, where

, and

are positive constants,

is the magnetization,

is the temperature, and

is the Curie temperature. The relation between

and

is best depicted by

Your answerChoose one option.

Diagram for Physics question 38 (figure 2)

Diagram for Physics question 38 (figure 3)

Diagram for Physics question 38 (figure 4)

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Consider a spherical galaxy of total mass

and radius

, having a uniform matter distribution. In this idealized situation, the orbital speed

of a star of mass

(

) as a function of the distance

from the galactic centre is best described by

(

is the universal gravitational constant)

Your answerChoose one option.

Diagram for Physics question 39 (figure 2)

Diagram for Physics question 39 (figure 3)

Diagram for Physics question 39 (figure 4)

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Consider the potential

defined as

where

and

are real constants of appropriate dimensions. According to the first Born approximation, the elastic scattering amplitude calculated with

for a (wave-vector) momentum transfer

and

, is proportional to

(Useful integral:

)

Your answerChoose one option.

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As shown in the figure, inverse magnetic susceptibility

is plotted as a function of temperature

for three different materials in paramagnetic states.

(Curie temperature of ferromagnetic material

Néel temperature of antiferromagnetic material

)

Choose the correct statement from the following

Your answerChoose one option.

Material 1 is antiferromagnetic (

), 2 is paramagnetic, and 3 is ferromagnetic (

Material 1 is paramagnetic, 2 is antiferromagnetic (

), and 3 is ferromagnetic (

Material 1 ferromagnetic (

), 2 is antiferromagnetic (

), and 3 is paramagnetic.

Material 1 is ferromagnetic (

), 2 is paramagnetic, and 3 is antiferromagnetic (

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A function

is defined only for

. The Laplace transform of

whereas the Fourier transform of

The correct statement(s) is(are)

Your answerSelect all correct options. You can choose more than one.

The variable

is always real.

The variable

can be complex.

and

can never be made connected.

and

can be made connected.

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and

are two Hermitian matrices and there exists a matrix

, which diagonalizes both of them, such that

and

, where

and

are diagonal matrices. The correct statement(s) is(are)

Your answerSelect all correct options. You can choose more than one.

All the elements of both matrices

and

are real.

The matrix

can have complex eigenvalues.

The matrix

can have complex eigenvalues.

The matrices

and

commute.

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A uniform block of mass

slides on a smooth horizontal bar. Another mass

is connected to it by an inextensible string of length

of negligible mass, and is constrained to oscillate in the X-Y plane only. Neglect the sizes of the masses. The number of degrees of freedom of the system is two and the generalized coordinates are chosen as

and

, as shown in the figure.

and

are the generalized momenta corresponding to

and

, respectively, then the correct option(s) is(are)

Your answerSelect all correct options. You can choose more than one.

is conserved

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The Gell-Mann – Okuba mass formula defines the mass of baryons as

where

and

are constants,

represents the isospin and

represents the hypercharge. If the mass of

hyperons is same as that of

hyperons, then the correct option(s) is(are)

Your answerSelect all correct options. You can choose more than one.

does not depend on

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GATE PH purpose:exam-prep PYQs

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