GATE PH topic:physical-sciences PYQs & Answers — Page 12

Questions 111–120 of 650. Imported answers require independent review unless marked reviewed.

A system of three non-identical spin

particles has the Hamiltonian

, where

and

are the spin operators of particles labelled 1, 2 and 3 respectively and

is a constant with appropriate dimensions. The set of possible energy eigenvalues of the system is

Your answerChoose one option.

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Which of the following option(s) is/are correct for a Type I superconductor?

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

The phase transition to the normal state in the absence of a magnetic field is of second order

With increase in temperature, the critical magnetic field decreases linearly to zero

Below the critical temperature, the entropy in the superconducting state is less than that in the normal state

The phase transition to the normal state in the presence of a magnetic field is of first order

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Consider two hypothetical nuclei

and

undergoing

decay, resulting in nuclei

and

, respectively. The decay scheme and the corresponding

values of the nuclei are given in the figure. Which of the following option(s) is/are correct? (

is the total angular momentum and

is parity)

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

is Fermi transition and

is Fermi transition

is Fermi transition and

is Gamow-Teller transition

is Gamow-Teller transition and

is Fermi transition

is Gamow-Teller transition and

is Gamow-Teller transition

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A point charge

is placed at a distance

above an infinite, grounded conducting plate placed on the

plane at

. The electrostatic potential in

region is given by

, where

and

. Which of the following option(s) is/are correct?

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

The magnitude of the force experienced by the point charge

The electrostatic energy of the system is

The induced surface charge density on the plate is proportional to

The electrostatic potential

satisfies Poisson’s equation for

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In coordinates

, a contravariant second rank tensor

has non-zero diagonal components

and

, with all other components vanishing, and

being real constants. Here,

is time and

is space coordinate. Consider a Lorentz transformation

to another frame that moves with relative speed

in the

direction, so that

. If

and

are the diagonal components of

, then setting the speed of light

, and with

, which of the following option(s) is/are correct?

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

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The Lagrangian of a particle of mass

and charge

moving in a uniform magnetic field of magnitude

that points in the

direction, is given by

where

are the components of its velocity

. If

denote the conjugate momenta in the

directions and

is the Hamiltonian, which of the following option(s) is/are correct?

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

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A bead is constrained to move along a long, massless, frictionless horizontal rod parallel to the

axis. The rod itself is moving vertically upward along the

direction against gravity with a constant speed, starting from

, and remains horizontal. The conjugate momenta are denoted by

and the Hamiltonian by

. Which of the following option(s) is/are correct?

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

is the total energy of the system and is conserved

is the total energy of the system and is not conserved

is not the total energy of the system, but it is conserved

is not the total energy of the system and is not conserved

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In a one-dimensional Hamiltonian system with position

and momentum

, consider the canonical transformation

, where

and

are the new position and momentum, respectively. Which of the following option(s) regarding the generating function

is/are correct?

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

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The energy of a free, relativistic particle of rest mass

moving along the

axis in one dimension, is denoted by

. When moving in a given potential

, its Hamiltonian is

. In the presence of this potential, its speed is

, conjugate momentum

, and the Lagrangian

. Then, which of the following option(s) is/are correct?

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

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Consider the integral

where

is a complex variable and

are positive real numbers. The integral is taken over a unit circle with center at the origin. Which of the following option(s) is/are correct?

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

when

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GATE PH topic:physical-sciences PYQs

Question 46

Question 47

Question 48

Question 49

Question 50

Question 51

Question 52

Question 53

Question 54

Question 55