Questions 41–50 of 650. Imported answers require independent review unless marked reviewed.

Topic practice 650 questionsPage 5 of 65

Question 41

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The energy

and degeneracy

of the second excited state of a three-dimensional, isotropic quantum harmonic oscillator with angular frequency

are
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Question 42

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Two identical particles with a fixed total energy

are in thermal equilibrium in a one-dimensional harmonic oscillator potential

. Let the entropy of the particles be denoted by

if they are fermions with spin

and

if they are bosons with spin 0. Then, which of the following options is correct? (

is the Boltzmann constant)
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Question 43

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In the circuit shown,

Volts, where

is in seconds, which of the following options is correct? (take the op amp to be ideal)
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Question 44

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Considering the circuit and the associated signals measured at different pins (numbered as 1, 2, 3, 4, 5) shown in the figure, the correct option is
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Question 45

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A gas of

classical particles that can occupy energy levels

and

is in equilibrium with a reservoir at temperature

. From the schematics shown below, choose the correct dependence of the internal energy

on

.
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Question 46

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The Lagrangian

with the generalized coordinate

is transformed to

. Consider the following statements: (i) Expression for the canonical momentum does not change. (ii) The equation of the motion does not change. Which of the following options is correct for the above statements?
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Question 47

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An infinitely large thin sheet in the

-plane carries uniform positive charge density and is moving with constant velocity

in the

direction (see figure below). The direction of the corresponding Poynting vector is
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Question 48

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A positive point charge is fixed at the origin. At some distance from it on the

axis, a point dipole is kept pointing in the

direction. The force on the dipole is
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Question 49

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Two frames

(solid lines) and

(dashed lines) with common origin are shown in the figure below. Frame

is inertial while

is rotating about the common

-axis. There is a point mass fixed at

on the

-axis of the

frame. The magnitude of the centrifugal force and the Coriolis force experienced by the mass in the

frame is

and

, respectively. Which of the following options is correct for these forces?
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Question 50

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Which of the following operators is/are self-adjoint?
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