IIT JAM 2022 Physics (PH) Question Paper with Answer Key pdf is available for download. The exam was conducted by IIT Roorkee on February 13, 2022. In terms of difficulty level, IIT JAM Physics (PH) was of Moderate to High level. The question paper comprised a total of 60 questions.
IIT JAM 2022 Physics (PH) Question Paper with Answer Key PDFs
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The equation \( z^2 + \bar{z}^2 = 4 \) in the complex plane (where \( \bar{z} \) is the complex conjugate of \( z \)) represents
A rocket \( (S') \) moves at a speed of \( \frac{c}{2} \, m/s \) along the positive \( x \)-axis, where \( c \) is the speed of light. When it crosses the origin, the clocks attached to the rocket and the one with a stationary observer \( (S) \) located at \( x = 0 \) are both set to zero. If \( S \) observes an event at \( (x,t) \), the same event occurs in the \( S' \) frame at
Consider a classical ideal gas of \( N \) molecules in equilibrium at temperature \( T \). Each molecule has two energy levels, \( -\epsilon \) and \( \epsilon \). The mean energy of the gas is
At a temperature \( T \), let \( \beta \) and \( \kappa \) denote the volume expansivity and isothermal compressibility of a gas, respectively. Then \( \frac{\beta}{\kappa} \) is equal to
The resultant of the binary subtraction \( 1110101 - 0011110 \) is
Consider a particle trapped in a three-dimensional potential well such that \( U(x, y, z) = 0 \) for \( 0 \leq x \leq a \), \( 0 \leq y \leq a \), \( 0 \leq z \leq a \) and \( U(x, y, z) = \infty \) everywhere else. The degeneracy of the 5th excited state is
A particle of mass \( m \) and angular momentum \( L \) moves in space where its potential energy is \( U(r) = kr^2 \, (k > 0) \) and \( r \) is the radial coordinate. If the particle moves in a circular orbit, then the radius of the orbit is
Consider a two-dimensional force field \[ \mathbf{F}(x, y) = (5x^2 + ay^2 + bxy) \hat{i} + (4x^2 + 4xy + y^2) \hat{j} \]
If the force field is conservative, then the values of \( a \) and \( b \) are
Consider an electrostatic field \( \mathbf{E} \) in a region of space. Identify the INCORRECT statement.
Which one of the following figures correctly depicts the intensity distribution for Fraunhofer diffraction due to a single slit? Here, \( x \) denotes the distance from the center of the central fringe and \( I \) denotes the intensity.
The function \( f(x) = e^{\sin x} \) is expanded as a Taylor series in \( x \), around \( x = 0 \), in the form \( f(x) = \sum_{n=0}^{\infty} a_n x^n \). The value of \( a_0 + a_1 + a_2 \) is
Consider a unit circle \( C \) in the \( xy \)-plane, centered at the origin. The value of the integral \[ \oint_C \left[ (\sin x - y) dx - (\sin y - x) dy \right] \]
over the circle \( C \), traversed anticlockwise, is
The current through a series RL circuit, subjected to a constant emf \( \mathcal{E} \), obeys \[ L \frac{di}{dt} + Ri = \mathcal{E} \]
Let \( L = 1 \, mH \), \( R = 1 \, k\Omega \), and \( \mathcal{E} = 1 \, V \). The initial condition is \( i(0) = 0 \). At \( t = 1 \, \mu s \), the current in mA is
An ideal gas in equilibrium at temperature \( T \) expands isothermally to twice its initial volume. If \( \Delta S \), \( \Delta U \), and \( \Delta F \) denote the changes in its entropy, internal energy, and Helmholtz free energy respectively, then
In a dilute gas, the number of molecules with free path length \( \geq x \) is given by \[ N(x) = N_0 e^{-x/\lambda}, \] where \(N_0 \) is the total number of molecules and \( \lambda \) is the mean free path. The fraction of molecules with free path lengths between \( \lambda \) and \( 2\lambda \) is
Consider a quantum particle trapped in a one-dimensional potential well in the region \( [-L/2 < x < L/2] \), with infinitely high barriers at \( x = -L/2 \) and \( x = L/2 \). The stationary wave function for the ground state is \( \psi(x) = \sqrt{\frac{2}{L}} \cos \left( \frac{\pi x}{L} \right) \). The uncertainties in momentum and position satisfy
Consider a particle of mass \( m \) moving in a plane with a constant radial speed \( \dot{r} \) and a constant angular speed \( \dot{\theta} \). The acceleration of the particle in \( (r, \theta) \) coordinates is
A planet of mass \( m \) moves in an elliptical orbit. Its maximum and minimum distances from the Sun are \( R \) and \( r \), respectively. Let \( G \) denote the universal gravitational constant, and \( M \) the mass of the Sun. Assuming \( M \gg m \), the angular momentum of the planet with respect to the center of the Sun is
Consider a conical region of height \( h \) and base radius \( R \) with its vertex at the origin. Let the outward normal to its base be along the positive \( z \)-axis, as shown in the figure. A uniform magnetic field \( \mathbf{B} = B_0 \hat{z} \) exists everywhere. Then the magnetic flux through the base \( (\Phi_b) \) and that through the curved surface of the cone \( (\Phi_c) \) are
Consider a thin annular sheet, lying on the \( xy \)-plane, with \( R_1 \) and \( R_2 \) as its inner and outer radii, respectively. If the sheet carries a uniform surface-charge density \( \sigma \) and spins about the origin \( O \) with a constant angular velocity \( \mathbf{\omega} = \omega_0 \hat{z} \), then the total current flow on the sheet is
View Solution
The current in a rotating ring is given by the charge flowing per unit time. For an element of radius \( r \) and thickness \( dr \), the surface charge is: \[ dq = \sigma \cdot 2\pi r \, dr \]
The tangential velocity of this charge is \( v = r \omega_0 \), and the current element is: \[ dI = v dq = r \omega_0 \cdot \sigma \cdot 2\pi r \, dr = 2\pi \sigma \omega_0 r^2 \, dr \]
The total current is obtained by integrating from \( R_1 \) to \( R_2 \): \[ I = \int_{R_1}^{R_2} 2\pi \sigma \omega_0 r^2 \, dr = 2\pi \sigma \omega_0 \left[ \frac{r^3}{3} \right]_{R_1}^{R_2} = 2\pi \sigma \omega_0 \left( \frac{R_2^3 - R_1^3}{3} \right) \]
Thus, the correct answer is option (A).
Quick Tip: When calculating current in rotating charged bodies, use the formula for the current element and integrate over the radius to get the total current.
A radioactive nucleus has a decay constant \(\lambda\) and its radioactive daughter nucleus has a decay constant \(10\lambda\). At time \(t = 0\), \(N_0\) is the number of parent nuclei and there are no daughter nuclei present. \(N_1(t)\) and \(N_2(t)\) are the number of parent and daughter nuclei present at time \(t\), respectively. The ratio \(N_2(t)/N_1(t)\) is
A uniform magnetic field \(\vec{B} = B_0 \hat{z}\), where \(B_0 > 0\), exists as shown in the figure. A charged particle of mass \(m\) and charge \(q (q > 0)\) is released at the origin, in the \(yz\)-plane, with a velocity \(\vec{v}\) directed at an angle \(\theta = 45^\circ\) with respect to the positive \(z\)-axis. Ignoring gravity, which one of the following is TRUE.
For an ideal intrinsic semiconductor, the Fermi energy at 0 K
A circular loop of wire with radius \( R \) is centered at the origin of the \( xy \)-plane. The magnetic field at a point within the loop is \( \vec{B}(\rho, \phi, z, t) = k \rho^3 \hat{z} \), where \( k \) is a positive constant of appropriate dimensions. Neglecting the effects of any current induced in the loop, the magnitude of the induced emf in the loop at time \( t \) is
For the given circuit, \( R = 125 \, \Omega \), \( R_L = 470 \, \Omega \), \( V_Z = 9 \, V \), and \( I_{Z_{max}} = 65 \, mA \). The minimum and maximum values of the input voltage \( (V_{min} \) and \( V_{max}) \) for which the Zener diode will be in the "ON" state are
A square laminar sheet with side \(a\) and mass \(M\), has mass per unit area given by
\[ \sigma(x) = \sigma_0 \left( 1 - \frac{|x|}{a} \right) \quad (see figure). Moment of inertia of the sheet about y-axis is \]
A particle is subjected to two simple harmonic motions along the x and y axes, described by \[ x(t) = a \sin(2\omega t + \pi) \quad and \quad y(t) = 2a \sin(\omega t). \]
The resultant motion is given by
For a certain thermodynamic system, the internal energy \( U = PV \) and \(P\) is proportional to \( T^2 \). The entropy of the system is proportional to
The dispersion relation for certain type of waves is given by \[ \omega = \sqrt{k^2 + a^2}, \]
where \(k\) is the wave vector and \(a\) is a constant. Which one of the following sketches represents \(v_g\), the group velocity?
Consider a binary number with \(m\) digits, where \(m\) is an even number. This binary number has alternating 1's and 0's, with digit 1 in the highest place value. The decimal equivalent of this binary number is
Consider the \(2 \times 2\) matrix \[ M = \begin{pmatrix} 0 & a
a & b \end{pmatrix} \]
where \(a, b > 0\). Then,
In the Compton scattering of electrons, by photons incident with wavelength \( \lambda \),
The figure shows a section of the phase boundary separating the vapour (1) and liquid (2) states of water in the \(P-T\) plane. Here, \(C\) is the critical point. \( \mu_1, v_1 \) and \(s_1\) are the chemical potential, specific volume and specific entropy of the vapour phase respectively, while \( \mu_2, v_2 \) and \( s_2 \) respectively denote the same for the liquid phase. Then,
A particle is executing simple harmonic motion with time period \(T\). Let \(x\), \(v\), and \(a\) denote the displacement, velocity, and acceleration of the particle, respectively, at time \(t\). Then,
A linearly polarized light beam travels from origin to point \(A(1, 0, 0)\). At the point \(A\), the light is reflected by a mirror towards point \(B(1, -1, 0)\). A second mirror located at point \(B\) then reflects the light towards point \(C(1, -1, 1)\). Let \( \hat{n}(x, y, z) \) represent the direction of polarization of light at \( (x, y, z) \).
Let \( (r, \theta) \) denote the polar coordinates of a particle moving in a plane. If \( \hat{r} \) and \( \hat{\theta} \) represent the corresponding unit vectors, then
The electric field associated with an electromagnetic radiation is given by \[ E = a(1 + \cos(\omega_1 t)) \cos(\omega_2 t) \]
Which of the following frequencies are present in the field?
A string of length \( L \) is stretched between two points \( x = 0 \) and \( x = L \), and the endpoints are rigidly clamped. Which of the following can represent the displacement of the string from the equilibrium position?
The Boolean expression \( Y = PQR + QR' + P'QR + PQR' \) simplifies to
For an \( n \)-type silicon, an extrinsic semiconductor, the natural logarithm of normalized conductivity (\( \sigma \)) is plotted as a function of inverse temperature. Temperature interval-I corresponds to the intrinsic regime, interval-II corresponds to the saturation regime, and interval-III corresponds to the freeze-out regime, respectively. Then,
The integral \[ \int \int (x^2 + y^2) \, dx \, dy \quad over the area of a disk of radius 2 in the xy-plane is \, \_ \_ \_ \, \pi \]
For the given operational amplifier circuit \[ R_1 = 120 \, \Omega, \, R_2 = 1.5 \, k\Omega, \, V_s = 0.6 \, V, then the output current I_0 is \_ \_ \_ \, mA. \]
For an ideal gas, AB and CD are two isotherms at temperatures \(T_1\) and \(T_2\) (\(T_1 > T_2\)), respectively. AD and BC represent two adiabatic paths as shown in the figure. Let \( V_A, V_B, V_C, V_D \) be the volumes of the gas at A, B, C, and D respectively. If \[ \frac{V_C}{V_B} = 2, \quad then \quad \frac{V_D}{V_A} = \_ \_ \_. \]
A satellite is revolving around the Earth in a closed orbit. The height of the satellite above Earth's surface at perigee and apogee are 2500 km and 4500 km, respectively. Consider the radius of the Earth to be 6500 km. The eccentricity of the satellite’s orbit is _ _ _ (Round off to 1 decimal place).
Three masses \( m_1 = 1 \), \( m_2 = 2 \), and \( m_3 = 3 \) are located on the x-axis such that their center of mass is at \( x = 1 \). Another mass \( m_4 = 4 \) is placed at \( x_0 \) and the new center of mass is at \( x = 3 \). The value of \( x_0 \) is _ _ _ .
A normal human eye can distinguish two objects separated by 0.35 m when viewed from a distance of 1.0 km. The angular resolution of the eye is _ _ _ seconds (Round off to the nearest integer).
A rod with a proper length of 3 m moves along the x-axis, making an angle of \( 30^\circ \) with respect to the x-axis. If its speed is \( \frac{c}{2} \) m/s, where \( c \) is the speed of light, the change in length due to Lorentz contraction is _ _ _ m (Round off to 2 decimal places).
Consider the Bohr model of the hydrogen atom. The speed of an electron in the second orbit (\(n = 2\)) is _ _ _ \(\times 10^6 \) m/s (Round off to 2 decimal places).
Consider a unit circle \(C\) in the xy-plane with center at the origin. The line integral of the vector field, \[ \mathbf{F}(x, y, z) = -2y \hat{x} - 3z \hat{y} + xz \hat{z}, \]
taken anticlockwise over \(C\) is _ _ _ \(\pi\).
Consider a p-n junction at \( T = 300 \, K \). The saturation current density at reverse bias is \( -20 \, \mu A/cm^2 \). For this device, a current density of magnitude \( 10 \, \mu A/cm^2 \) is realized with a forward bias voltage, \( V_F \). The same magnitude of current density can also be realized with a reverse bias voltage, \( V_R \). The value of \[ \left| \frac{V_F}{V_R} \right| is \_ \_ \_ \, (Round off to 2 decimal places). \]
Consider the second-order ordinary differential equation, \[ y'' + 4y' + 5y = 0, \quad with \quad y(0) = 0 \quad and \quad y'(0) = 1. \quad Then the value of \quad y\left( \frac{\pi}{2} \right) \quad is \_ \_ \_ \, (Round off to 3 decimal places). \]
A box contains a mixture of two different ideal monoatomic gases, 1 and 2, in equilibrium at temperature \(T\). Both gases are present in equal proportions. The atomic mass for gas 1 is \(m\), while the same for gas 2 is \(2m\). If the rms speed of a gas molecule selected at random is \( v_{rms} = \sqrt{\frac{k_B T}{m}} \), then \( x \) is _ _ _ (Round off to 2 decimal places).
A hot body with constant heat capacity 800 J/K at temperature 925 K is dropped gently into a vessel containing 1 kg of water at temperature 300 K and the combined system is allowed to reach equilibrium. The change in the total entropy \( \Delta S \) is _ _ _ J/K (Round off to 1 decimal place).
Consider an electron with mass \( m \) and energy \( E \) moving along the \( x \)-axis towards a finite step potential of height \( U_0 \) as shown in the figure. In region 1 (\( x < 0 \)), the momentum of the electron is \( p_1 = \sqrt{2mE} \). The reflection coefficient at the barrier is given by \[ R = \left( \frac{p_1 - p_2}{p_1 + p_2} \right)^2, \quad where \, p_2 \, is the momentum in region 2. \]
If, in the limit \( E \gg U_0 \), \[ R \approx \frac{U_0^2}{n^2 E^2}, \]
then the integer \( n \) is _ _ _.
A current density for a fluid flow is given by, \[ \mathbf{J}(x, y, z, t) = \frac{8e^t}{(1 + x^2 + y^2 + z^2)} \hat{x}. \]
At time \( t = 0 \), the mass density \( \rho(x, y, z, 0) = 1 \). Using the equation of continuity, \( \rho(1, 1, 1, 1) \) is found to be _ _ _ (Round off to 2 decimal places).
The work done in moving a \( -5 \, \mu C \) charge in an electric field \[ \mathbf{E} = (8r \sin \theta \hat{r} + 4r \cos \theta \hat{\theta}) \, V/m, \]
from a point \( A(r, \theta) = (10, \frac{\pi}{6}) \) to a point \( B(r, \theta) = (10, \frac{\pi}{2}) \) is _ _ _ mJ.
A pipe of 1 m length is closed at one end. The air column in the pipe resonates at its fundamental frequency of 400 Hz. The number of nodes in the sound wave formed in the pipe is _ _ _ .
View Solution
Step 1: Understanding the Fundamentals.
For a pipe closed at one end, the fundamental frequency corresponds to the first harmonic. The number of nodes in the sound wave formed in the pipe is determined by the standing wave pattern. For a pipe closed at one end, there is one node at the closed end and one antinode at the open end.
Step 2: Using the Formula for Fundamental Frequency.
The fundamental frequency \( f \) of a pipe closed at one end is given by: \[ f = \frac{v}{4L} \]
where:
- \( v = 320 \, m/s \) is the speed of sound,
- \( L = 1 \, m \) is the length of the pipe.
Substituting the values: \[ 400 = \frac{320}{4 \times 1}. \]
Thus, the number of nodes is \( 2 \).
Step 3: Conclusion.
Thus, the number of nodes is \( \boxed{2} \). Quick Tip: For a pipe closed at one end, the number of nodes is always one more than the number of half-wavelengths.
The critical angle of a crystal is \( 30^\circ \). Its Brewster angle is _ _ _ degrees (Round off to the nearest integer).
In an LCR series circuit, a non-inductive resistor of 150 \(\Omega\), a coil of 0.2 H inductance and negligible resistance, and a 30 \(\mu F\) capacitor are connected across an ac power source of 220 V, 50 Hz. The power loss across the resistor is _ _ _ W (Round off to 2 decimal places).
A charge \( q \) is uniformly distributed over the volume of a dielectric sphere of radius \( a \). If the dielectric constant \( \varepsilon_r = 2 \), then the ratio of the electrostatic energy stored inside the sphere to that stored outside is _ _ _ (Round off to 1 decimal place).
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