GATE PH purpose:exam-prep PYQs & Answers — Page 31

Questions 301–310 of 650. Imported answers require independent review unless marked reviewed.

A particle of mass 1 kg is released from a height of 1 m above the ground. When it reaches the ground, what is the value of Hamilton’s action for this motion in J s? (

is the acceleration due to gravity; take gravitation potential to be zero on the ground)

Your answerChoose one option.

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is a constant of motion of a two-dimensional isotropic harmonic oscillator with Lagrangian

then

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In a two-dimensional square lattice, frequency

of phonons in the long wavelength limit changes linearly with the wave vector

. Then the density of states of phonons is proportional to

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K, which of the following diagram represents the occupation probability

of energy states of electrons in a BCS type superconductor?

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Diagram for Physics question 44 (figure 2)

Diagram for Physics question 44 (figure 3)

Diagram for Physics question 44 (figure 4)

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For a one-dimensional harmonic oscillator, the creation operator (

) acting on the

state

, where

, gives

. The matrix representation of the position operator

for the first three rows and columns is

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A piston of mass

is fitted to an airtight horizontal cylindrical jar. The cylinder and piston have identical unit area of cross-section. The gas inside the jar has volume

and is held at pressure

. The piston is pushed inside the jar very slowly over a small distance. On releasing, the piston performs an undamped simple harmonic motion of low frequency. Assuming that the gas is ideal and no heat is exchanged with the atmosphere, the frequency of the small oscillations is proportional to

Your answerChoose one option.

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A paramagnetic salt of mass

is held at temperature

in a magnetic field

. If

is the entropy of the salt and

is its magnetization, then

, where

is the Gibbs free energy. If the magnetic field is changed adiabatically by

and the corresponding infinitesimal changes in entropy and temperature are

and

, then which of the following statements are correct

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A particle of mass

is moving inside a hollow spherical shell of radius

so that the potential is

The ground state energy and wavefunction of the particle are

and

, respectively. Then which of the following options are correct?

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A particle of unit mass moves in a potential

. If the angular momentum of the particle is

, then which of the following statements are true?

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There are two equilibrium points along the radial coordinate

There is one stable equilibrium point at

and one unstable equilibrium point at

There are two stable equilibrium points along the radial coordinate

There is only one equilibrium point along the radial coordinate

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In a diatomic molecule of mass

, electronic, rotational and vibrational energy scales are of magnitude

and

, respectively. The spring constant for the vibrational energy is determined by

. If the electron mass is

then

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GATE PH purpose:exam-prep PYQs

Question 41

Question 42

Question 43

Question 44

Question 45

Question 46

Question 47

Question 48

Question 49

Question 50