List of top Physics Questions asked in IIT JAM

A rod of mass 𝑀, length 𝐿 and non-uniform mass per unit length \(λ(x)=\frac{3Mx^2}{L^3},\) is held horizontally by a pivot, as shown in the figure, and is free to move in the plane of the figure. For this rod, which of the following statements are true?

A single pendulum hanging vertically in an elevator has a time period 𝑇₀ when the elevator is stationary. If the elevator moves upward with an acceleration of 𝑎 = 0.2𝑔, the time period of oscillations is 𝑇₁. Here 𝑔 is the acceleration due to gravity. The ratio\( \frac{𝑇_0}{ 𝑇_1}\) is (rounded off to two decimal places).

Consider a spring mass system with mass 0.5 kg and spring constant 𝑘 = 2 Nm^-1 in a viscous medium with drag coefficient 𝑏 = 3 kg s ^-1 . The additional mass required so that the motion becomes critically damped is _______ kg (rounded off to three decimal places)

The lattice constant (in Å) of copper, which has FCC structure, is _________ (rounded off to two decimal places).
Given: density of copper is 8.91 g cm^-3 and its atomic mass is 63.55 g mol^-1 ; Avogadro’s number = 6.023 × 10²³ mol⁻¹

The absolute error in the value of sin𝜃 if approximated up to two terms in the Taylor’s series for 𝜃 = 60∘ is ___________ (rounded off to three decimal places).

The sum of the x-components of unit vectors 𝑟̂ ̇ and 𝜃̂̇ for a particle moving with angular speed 2 rad s ^-1 at angle 𝜃 = 215° is__________ (rounded off to two decimal places)

A conducting wire AB of length m has resistance of .6 Ω. It is connected to a voltage source of 0.5 V with negligible resistance as shown in the figure. The corresponding electric and magnetic fields give Poynting vectors 𝑆 (𝑟 ) all around the wire. Surface integral ∫ 𝑆 . 𝑑𝑎 is calculated over a virtual sphere of diameter 0.2 m with its centre on the wire, as shown. The value of the integral is ______W (rounded off to three decimal places)

A uniform stick of length l and mass m pivoted at its top end is oscillating with an angular frequency ω_r . Assuming small oscillations, the ratio ω_r/ω_s , where ω_s is the angular frequency of a simple pendulum of the same length, will be

A fission device explodes into two pieces of rest masses 𝑚 and 0.5𝑚 with no loss of energy into any other form. These masses move apart respectively with speeds \(\frac{c}{ √13} \) and \(\frac{c}{2}\) , with respect to the stationary frame. If the rest mass of the device is 𝑓𝑚 then 𝑓 is________ (rounded off to two decimal places).

A container is occupied by a fixed number of non-interacting particles. If they are obeying Fermi-Dirac, Bose-Einstein, and Maxwell-Boltzmann statistics, the pressure in the container is P_FD, P_BE and P_MB, respectively. Then

In a X-Ray tube operating at 20 kV, the ratio of the de-Broglie wavelength of the incident electrons to the shortest wavelength of the generated X-rays is ________ (rounded off to two decimal places).
Given: e/m ratio for an electron = 1.76×10¹¹ Ckg-1 and the speed of light in vacuum is 3×10⁸ ms ^-1

The sum of the eigenvalues 𝜆₁ and 𝜆₂ of matrix 𝐵 = 𝐼+𝐴+𝐴² , where
\( \left[ {\begin{array}{cc}  2&1 \\     -0.5 &0.5 \\   \end{array} } \right]\)
 is_____ (rounded off to two decimal places).

A point source emitting photons of 2 eV energy and 1 W of power is kept at a distance of 1m from a small piece of a photoelectric material of area 10^-4 m² . If the efficiency of generation of photoelectrons is 10%, then the number of photoelectrons generated are 𝑓×10¹² per second. The value of 𝑓 is __________ (rounded off to two decimal places).
Given: 1eV = 1.6 × 10⁻¹⁹ J

A small bar magnet is dropped through different hollow copper tubes with same length and inner diameter but with different outer diameter. The variation in the time (t) taken for the magnet to reach the bottom of the tube depends on its wall thickness (d) as

Suppose the divergence of magnetic field \(\vec{𝐵}\) is nonzero and is given as \(∇⃗.\vec{𝐵} = \mu_0\rho_m\), where 𝜇₀ is the permeability of vacuum and 𝜌_m is the magnetic charge density. If the corresponding magnetic current density is \(\vec{J}_𝑚\), then the curl \(∇⃗ × \vec{𝐸}\) of the electric field \(\vec{𝐸}\) is

Three frames 𝐹₀, 𝐹₁ and 𝐹₂ are in relative motion. The frame 𝐹₀ is at rest, 𝐹₁ is moving with velocity 𝑣1𝑖̂with respect to 𝐹₀ and 𝐹₂ is moving with velocity 𝑣₂𝑖̂ with respect to 𝐹₁. A particle is moving with velocity 𝑣3𝑖̂ with respect to 𝐹₂. If 𝑣₁ = 𝑣₂ = 𝑣₃= \(\frac{𝑐}{2}\), where 𝑐 is the speed of light, the speed of the particle with respect to 𝐹₀ is 𝑓𝑐. The value of 𝑓 is ____________ (rounded off to two decimal places)

Consider a system of large number of particles that can be in three energy states with energies 0 meV, 1 meV, and 2 meV. At temperature T = 300 K, the mean energy of the system (in meV) is closest to
Given: Boltzmann constant k_B = 0.086 meVK^-1

Consider the 𝛼-decay ⁹⁰𝑇ℎ ²³²→⁸⁸𝑅𝑎 ²²⁸ . In an experiment with one gram of ⁹⁰𝑇ℎ ²³², the average count rate (integrated over the entire volume) measured by the 𝛼-detector is 3000 counts s ^-1 . If the half life of ⁹⁰𝑇ℎ ²³² is given as 4.4 × 10¹⁷ s, then the efficiency of the 𝛼-detector is ______(rounded off to two decimal places).
Given: Avogadro’s number = 6.023 × 1023 mol⁻¹

A container of volume 𝑉 has helium gas in it with 𝑁 number of He atoms. The mean free path of these atoms is 𝜆_He. Another container has argon gas with the same number of Ar atoms in volume 2𝑉 with their mean free path being 𝜆_Ar. Taking the radius of Ar atoms to be 1.5 times the radius of He atoms, the ratio 𝜆_Ar⁄𝜆_He is__________ (rounded off to two decimal places).

In the Thomson model of hydrogen atom, the nuclear charge is distributed uniformly over a sphere of radius 𝑅. The average potential energy of an electron confined within this atom can be taken as \(V=\frac{e^2}{4{\pi}e_0R}\) . Taking the uncertainty in position to be the radius of the atom, the minimum value of 𝑅 for which an electron will be confined within the atom is estimated to be 𝑓 × 10⁻¹¹ m. The value of 𝑓 is _______ (rounded off to one decimal place). 
Given: The uncertainty product of momentum and position is ℏ = 1×10⁻³⁴ Js ^-1 ,e=1.6 × 10⁻¹⁹C, and \(\frac{1}{4{\pi}e_0}\)= 9 × 10⁹ Nm2C ⁻²

For the Maxwell-Boltzmann speed distribution, the ratio of the root-mean-square speed (v_rms) and the most probable speed (v_max) is
Given : Maxwell-Boltzmann speed distribution function for a collection of particles of mass m is
\(f(v)=(\frac{m}{2\pi k_BT})^{3/2}4\pi v^2\text{exp}(-\frac{mv^2}{2k_BT})\)
where, v is the speed and k_BT is the thermal energy.

For a given vector \(\vec{F}=-y\hat{i}+z\hat{j}+x^2\hat{k}\) , the surface integral \(\int_S(\vec{▽}\times \vec{F}).\hat{r}dS\) over the surface S of a hemisphere of radius R with the centre of the base at the origin is

Inverse of the matrix \(\begin{bmatrix} 1 & 1 & 0 \\ 2 & 3 & 0 \\ 1 & 0 & 1 \end{bmatrix}\) is

Two digital inputs A and B are given to the following circuit. For A = 1, B = 0, the values of X and Y are :

In a dielectric medium of relative permittivity 5, the amplitudes of the displacement current and conduction current are equal for an applied sinusoidal voltage of frequency f = 1 MHz. The value of conductivity (in Ω^-1m^-1) of the medium at this frequency is