CSIR NET 2024 - June 24 NET Physics

The evolution of the dynamical variables $x(t)$ and $p(t)$ is given by

$\dot{x} = ax$

$\dot{p} = -p$

where $a$ is

A uniform plane square sheet of mass $m$ is centered at the origin of an inertial frame. The sheet is rotating about an

A body of mass $m$ is acted upon by a central force $\vec{f}(\vec{r}) = -k \vec{r}$, where $k$ is a positive constant. I

A square plate of dimension $a \times a$ makes an angle $\theta = \pi/4$ with the $x$ axis in its rest frame $S$. It is

The Hamiltonian for a one-dimensional simple harmonic oscillator is given by $H = \frac{p^2}{2m} + \frac{1}{2}m\omega^2x

If $A$ and $B$ are hermitian operators and $C$ is an antihermitian operator, then:

If $\vec{L}$ is the orbital angular momentum operator and $\vec{\sigma}$ are the Pauli matrices, which of the following

A quantum mechanical system is in the angular momentum state $|l=4, l_z=4\rangle$. The uncertainty in $L_x$ is

A hydrogen atom is in the state $|\psi\rangle = \sqrt{\frac{8}{21}}|\psi_{200}\rangle + \sqrt{\frac{3}{7}}|\psi_{210}\ra

Probability density function of a variable $x$ is given by $P(x) = \frac{1}{2}[\delta(x-a) + \delta(x+a)]$. The variance

Vorticity of a vector field $\vec{B}$ is defined as $\vec{\omega} = \nabla \times \vec{B}$. Given $\vec{B} = kxyz\hat{r}

The matrix $A$ is given by $A = \begin{pmatrix} 1 & 2 & -3 \\ 0 & 3 & 2 \\ 0 & 0 & -2 \end{pmatrix}$. The eigenvalues of

An integral is given by $\int_{-\infty}^{\infty} dx \int_{-\infty}^{\infty} dy \exp[-(x^2 + y^2 + 2axy)]$, where $a$ is

The region $y > 0$ has a constant electrostatic potential $V_1$ and $y < 0$ has a constant electrostatic potential $V_2

The electric field of an electromagnetic wave in free space is given by $\vec{E} = E_0 \sin(\omega t - k_z z)\hat{j}$. T

A point electric dipole $\vec{P} = p_x\hat{i}$ is placed at a vertical distance $d$ above a grounded infinite conducting

A finite sized light source is used in a double slit experiment. The observed intensity pattern changes from figure (a)

Quantum particles of unit mass, in a potential $$V(x) = \begin{cases} \frac{1}{2}\omega^2x^2 & x > 0 \ \infty & x \le 0

A single particle can exist in two states with energies $0$ and $E$ respectively. At high temperatures ($k_BT \gg E$) th

The following $P - V$ diagram shows a process, where an ideal gas is taken quasi-statically from $A$ to $B$ along the pa

Two non-interacting classical particles having masses $m_1$ and $m_2$ are moving in a one-dimensional box of length $L$.

A set of 100 data points yields an average $\bar{x} = 9$ and a standard deviation $\sigma_x = 4$. The error in the estim

A battery with an open circuit voltage of $10 V$ is connected to a load resistor of $485\Omega$ and the voltage measured

The logic levels $H$ and $L$ at different locations in a digital circuit are found to be as shown in the figure. Based o

A train of square wave pulses is given to the input of an ideal op-amp circuit shown below. Given that the time period o

A particle of mass $m$ is moving in a potential $V(r) = -\frac{k}{r}$, where $k$ is a positive constant. If $\vec{L}$ an

A linear molecule is modelled as two atoms of equal mass $m$ placed at coordinates $x_1$ and $x_2$, connected by a sprin

For a simple harmonic oscillator, the Lagrangian is given by $L = \frac{1}{2}\dot{q}^2 - \frac{1}{2}q^2$. If $H(q, p)$ i

Three identical simple pendula (of mass $m$ and equilibrium string length $l$) are attached together by springs of sprin

Using a normalized trial wavefunction $\psi(x) = \sqrt{a}e^{-a|x|}$ (where $a$ is a positive real constant) for a partic

The Hamiltonian of a particle of mass $m$ is given by $H = \frac{p^2}{2m} + V(x)$, with $V(x) = \begin{cases} -\alpha x

A particle of energy $E$ is scattered off a one-dimensional potential $\lambda\delta(x)$, where $\lambda$ is a real posi

The following four matrices form a representation of a group $$I = \begin{pmatrix} 1 & 0 \ 0 & 1 \end{pmatrix}, A = \be

An integral transform $\tilde{f}(x)$ of a function $f(x)$ can be regarded as a result of applying an operator $F$ to the

The general solution for the second order differential equation $\frac{d^2y}{dx^2} - y = x\sin x$ will be (where $C_1$ a

The integral $I = \int_0^1 \frac{2x}{1+x^2} dx$ is estimated using Simpson's $1/3$rd rule with a grid value of $h = 0.5$

In a non-magnetic material with no free charges and no free currents, the permittivity $\epsilon$ is a function of posit

A radio station antenna on the earth's surface radiates 50 kW power isotropically. Assume the electromagnetic waves to b

A particle of unit mass and unit charge is moving in a magnetic field, which varies as $\vec{B}(\vec{r}) = b_0 \vec{r} /

A two-dimensional sheet with a uniform sheet conductivity of $\sigma$ has a central metallic point contact and a circula

Rotational energy of a molecule in the angular momentum state $j$ is given by $E_j = \frac{\hbar^2}{2I}j(j+1)$, where $I

A random walker takes a step of unit length towards right or left at any discrete time step. Starting from $x=0$ at time

Five classical spins are placed at the vertices of a regular pentagon. The Hamiltonian of the system is $H = J \sum S_i

A piezoresistive pressure sensor utilizes change in electrical resistance ($\Delta R$) with change in pressure ($\Delta

In the circuit shown in the figure, the resistances $R$ and $R'$ change due to strain. While $R$ increases, $R'$ decreas

An astronomer observes 500 objects and classifies them as either of type A or type B. She finds 148 objects to be of typ

The Debye temperature of a two-dimensional insulator is $150 \text{ K}$. The ratio of the heat required to raise its tem

Consider a body-centered tetragonal lattice with lattice constants $a = b = a_0$ and $c = \frac{a_0}{2}$. The number of

The band dispersion of electrons in a two-dimensional square lattice (lattice constant $a$) is given by, $$E(k_x, k_y) =

The bond dissociation energy of a molecule is defined as the energy required to dissociate it. For $H_2$ and $H_2^+$ mol

Helium atom is excited to a state with the configuration $(2s2p)$ with an energy $58.3$ eV. After some time, this atom s

An atom of mass $m$, initially at rest, resonantly absorbs a photon. It makes a transition from the ground state to an e

In a scattering experiment a beam of $e^-$ with an energy of 420 MeV scatters off an atomic nucleus. If the first minimu

$\pi^{-}$ has spin 0 and negative intrinsic parity. In a reaction a deuteron in its ground state ($J=1$, parity is +1) c

The $\Delta^{++}$ can be produced by colliding a pion beam onto a $H_2$ target, in a reaction $\pi^+ + p \rightarrow \De