List of top Physics Questions asked in GATE Physics

Two point charges of charge \( +q \) each are placed a distance \( 2d \) apart. A grounded solid conducting sphere of radius \( a \) is placed midway between them. Assume \( a^2 \ll d^2 \). Which of the following statements is/are true?

A particle of mass m is moving in the potential
\[ V(x) = \begin{cases} V_0 + \frac{1}{2} m \omega_{0P}^2 x^2 & \quad \text{if } x > 0 \\\infty & \quad \text{if } x \leq 0 \end{cases}\]
Figures P, Q, R, and S show different combinations of the values of \( \omega_0 \) and \( V_0 \).

Let \( E^{(P)}_j \), \( E^{(Q)}_j \), \( E^{(R)}_j \), and \( E^{(S)}_j \) with \( j = 0, 1, 2, \ldots \), be the eigen-energies of the j-th level for the potentials shown in Figures P, Q, R, and S, respectively. Which of the following statements is/are true?

A particle of mass \( m \) in an infinite potential well of width \( a \) is subjected to a perturbation \( V' = \frac{h^2}{40ma^2} \) as shown in the figure, where \( h \) is Planck's constant.

The first-order energy shift of the fourth energy eigenstate due to this perturbation is \( \frac{h^2}{Nma^2} \). The value of \( N \) is ____ (in integer).

An electron in the Coulomb field of a proton is in the following state of coherent superposition of orthonormal states \( \psi_{n i m} \):\[ \psi = \frac{1}{3} \psi_{100} + \frac{1}{\sqrt{3}} \psi_{210} + \frac{\sqrt{5}}{3} \psi_{320} \]Let \( E_1, E_2, \) and \( E_3 \) represent the first three energy levels of the system. A sequence of measurements is done on the same system at different times. Energy is measured first at time \( t_1 \) and the outcome is \( E_2 \). Then total angular momentum is measured at time \( t_2 > t_1 \), and finally, energy is measured again at \( t_3 > t_2 \). The probability of finding the system in a state with energy \( E_2 \) after the final measurement is \( \frac{P}{9} \). The value of \( P \) is ______ (in integer).

The Lagrangian of a particle of mass \( m \) is given by \( L = \frac{1}{2}m\dot{x}^2 - \lambda x^4 \), where \( \lambda \) is a positive constant. If the particle oscillates with total energy \( E \), then the time period of oscillations \( T \) is given by:
\[ T = a \int_0^{\left(\frac{E}{\lambda}\right)^{\frac{1}{4}}} \frac{dx}{\sqrt{\frac{2}{m}(E - \lambda x^4)}} \]
The value of \( a \) is ___ (in integer).

The typical biasing of a silicon transistor is shown in the figure.

The value of the common-emitter current gain \( \beta \) for the transistor is 100. Ignore reverse saturation current. The output voltage \( V_o \) (in V) is ____ (in integer).

The temperature \( T \) dependence of magnetic susceptibility \( \chi \) (Column I) of certain magnetic materials (Column II) are given below. Which of the following options is/are correct?

Column I	Column II
(1)	(P) Diamagnetic
(2)	(Q) Paramagnetic
(3)	(R) Ferromagnetic
(4)	(S) Antiferromagnetic

A material behaves as a superconductor below a critical temperature \( T_c \) and as a normal conductor above \( T_c \). A magnetic field \(\overrightarrow{B} = B\hat{z}\) is applied when \( T > T_c \). The material is then cooled below \( T_c \) in the presence of \( \vec{B} \). Which of the following figures represents the correct configuration of magnetic field lines?

The curves \( P \) and \( Q \) schematically show the variation of X-ray intensity with wavelength at two different accelerating voltages for a given target material. In the figure, \( \lambda_1 = 0.25 \) Å, \( \lambda_2 = 0.5 \) Å, \( \lambda_3 = 1.0 \) Å, and \( \lambda_4 = 2.25 \) Å. Take Planck's constant as \( 6.6 \times 10^{-34} \) Js, the speed of light as \( 3 \times 10^8 \) m/s, and the elementary charge as \( 1.6 \times 10^{-19} \) C.

Which of the following statement is/are true?

An oscillating electric dipole of moment \(\overrightarrow{d}(t) = d_0 \cos(\omega t) \hat{z}\) is placed at the origin as shown in the figure. Consider a point \(P(r, \theta, \phi)\) at a very large distance from the dipole. Here, \(r\), \(\theta\), and \(\phi\) are spherical polar coordinates. Which of the following statements is/are true for the intensity of radiation?

The canonical partition function of an ideal gas is given by \( Q(T,V,N) = \frac{1}{N!} \left( \frac{V}{\lambda(T)^3} \right)^N \), where \( T \), \( V \), \( N \), and \( \lambda(T) \) denote temperature, volume, number of particles, and thermal de Broglie wavelength, respectively. Let \( k_B \) be the Boltzmann constant and \( \mu \) be the chemical potential. Using \( \ln(N!) = N \ln(N) - N \), if the number density \( \left( \frac{N}{V} \right) \) is \( 2.5 \times 10^{25} \) m\(^{-3} \) at temperature \( T \), then \( e^{\mu/(k_B T)} / (\lambda(T))^3 \times 10^{-25} \) is ___ m\(^{-3} \) (rounded off to one decimal place).

Decays of mesons and baryons can be categorized as weak, strong and electromagnetic decays depending upon the interactions involved in the processes. Which of the following option is/are true?

An infinite one-dimensional lattice extends along the x-axis. At each lattice site, there exists an ion with spin 1/2. The spin can point either in the +z or -z direction only. Let \( S_P \), \( S_F \), and \( S_A \) denote the entropies of paramagnetic, ferromagnetic, and antiferromagnetic configurations, respectively. Which of the following relations is/are true?