List of top Physics Questions asked in IISER

Three infinite plane sheets which have uniform positive surface charge densities $\sigma$, $\sigma$ and $2\sigma$, are arranged parallel to each other with a separation of $d$ as shown in the figure. A spherical Gaussian surface $S$ of radius $d/2$ has its center on the middle sheet. Which of the following statements regarding the electric flux $\Phi_L$ through the left hemisphere and the electric flux $\Phi_R$ through the right hemisphere of the Gaussian surface is correct?

The three numbers: (number of protons, number of neutrons, the radius) characterize a nucleus. What is the value of $\frac{r_1}{r_2}$ for two nuclei characterized by $(1, 0, r_1)$ and $(4, 4, r_2)$?

Consider normal incidence of a monochromatic beam of photons of power $P$ on a flat surface. Of the incident beam, 10% gets absorbed, 10% gets transmitted, and the rest is reflected by the flat surface. If $c$ is the speed of light, what is the force exerted on the flat surface by the beam?

Consider two Carnot engines of efficiencies $\eta_1$ and $\eta_2$. The first engine absorbs heat $Q_1$ from a heat reservoir A and releases heat $Q_2$ to a heat reservoir B. The second engine takes heat $Q_2$ from B and releases heat $Q_3$ to a heat reservoir C. If $Q_1 > Q_2 > Q_3$, what is the net efficiency of this combination of the two Carnot engines?

The acceleration of a point particle is given by the equation \[ \frac{d^2\mathbf{x}}{dt^2} = \alpha \frac{\mathbf{x}}{|\mathbf{x}|^7} + \beta \frac{d\mathbf{x}}{dt} \] where $\mathbf{x}$ denotes position and $t$ denotes time. Which of the following relations show the correct dimensions for $\alpha$ and $\beta$?

An experimental study of the photoelectric effect involves a metal of work function $\phi_0$. What is the smallest wavelength of the incident photon to photoemit an electron of mass $m$ which has the same de Broglie wavelength as that of the incident photon? [Given $h$ is the Planck's constant, $c$ is the speed of light, and $\phi_0 \ll mc^2$]

A jar is filled with two monoatomic non-interacting gases A and B with total masses $M_A$ and $M_B$, respectively. The molar mass of A is double the molar mass of B. If the jar is kept at temperature $T$, what is the ratio of the total pressure of the combined gas to the partial pressure due to the gas A?

A planet is revolving in a circular orbit with a time period $T$ around the center of a star solely under the gravity of the star. Suppose the distance between the star and the planet is halved. The individual radii of the star and the planet are also halved, keeping their uniform mass densities unchanged. What will be the time period of the new orbit of the planet?

A long solenoid of initial radius $R_0$ is put in a region of uniform magnetic field $\mathbf{B}$ with the axis of the solenoid aligned along the magnetic field. The solenoid is a part of a closed circuit that has no initial current running through it. If the radius of the solenoid starts increasing at a uniform rate, how do the magnetic field strength $B_{in}$ and the associated magnetic energy $U_{in}$ inside the solenoid change?

An exotic spherical jellyfish has a bulk modulus $B$. Close to the surface of the sea (depth $d=0$), its radius is $R$. When it dives to a depth $d$ ($d \gg R$), its radius is reduced by $\Delta R > 0$. Given the density of the incompressible sea water $\rho$, and the uniform acceleration due to gravity $g$ such that $\rho g d \ll B$, what is $\frac{\Delta R}{R}$?

The position of a particle of mass 1 kg at time $t$ is given by $\mathbf{r} = t\hat{i} + \hat{j} + 2t^2\hat{k}$, where $t$ is in seconds and the coefficients have the proper units for $\mathbf{r}$ to be in metres. What is the component of the angular momentum (with respect to the origin) in kg m$^2$ s$^{-1}$ along the vector $(\hat{i} + \hat{j})$?

A simple pendulum of length $L$, mass $m$ and electric charge $q$ on its bob is oscillating with a time period $T$ under uniform gravity which is in the $-\hat{z}$ direction. Upon applying a uniform electric field $|E|\hat{n}$ (where $\hat{n}$ is a unit vector in the plane of oscillation), the time period of the pendulum decreases. Which of the following statements is NOT correct?

A particle of mass $m_1$ and electric charge $q$ starts from rest under the influence of a uniform external electric field $\mathbf{E}$ to travel a distance $d$ in time $t_1$. If the particle had mass $m_2$, it would take time $t_2$ to travel the same distance. What is the ratio $\frac{t_1}{t_2}$?

A sphere and a cube of equal masses on a horizontal frictionless floor, are confined between two vertical walls, as shown in the figure. The cube is attached to the wall by a massless spring. At the equilibrium position of the spring, the sphere just touches the cube. The cube is moved towards the left by a small amount $\ell$ from its equilibrium position, compressing the spring and is released at $t = 0$. The system keeps returning to its initial configuration as that of $t = 0$ with a time period $T$. If all the collisions are elastic, which of the following statements is correct?

A spherical concave mirror of focal length 10 cm and a double convex lens of focal length 5 cm are arranged on the common principal axis as shown in the figure. A small object is placed on the principal axis between the focal points $F_1$ and $F_2$ of the mirror and the lens, respectively. If two real and mutually inverted images are formed by the lens at the same location on the principal axis, what is the distance of the object from the mirror on the principal axis?

An electron in the ground state (with energy $E_1$) of a hydrogen atom, absorbs a photon of energy $E_a$, and gets excited to a higher energy level of principal quantum number $n$. What is the value of $n$?

What is the potential difference between the points $P$ and $Q$ in the circuit shown below, once the capacitors are fully charged?

Consider an equilateral prism of refractive index 1.5 and a parallelepiped block of refractive index 2.0 arranged as shown in the figure such that their adjacent faces are parallel. A light ray enters the prism from air at an angle of incidence such that the ray travels through the prism parallel to its base. What is the angle of emergence $\theta$?

A source produces a light beam of intensity $I_0$ polarized along the $x$-direction. The beam is sent along the $z$-direction. It enters a polaroid $P_1$ with its polaroid axis aligned along the $y$-direction so that no light exits the polaroid. When another polaroid $P_2$ is placed in between the source and $P_1$, the intensity measured after $P_1$ is $3I_0/16$. Which among the following is a possible value of $\theta$, the angle of the polaroid axis measured from the $x$-axis?

A charged particle is moving in a circular orbit with radius $r$ and orbital angular frequency $\omega$ in the presence of a magnetic field. The orbit is enclosed within a larger circular metallic frame. The frame is concentric and coplanar with the orbit. The radius of the frame is now gradually decreased. Assuming that the particle remains within the frame at all times, what changes to the trajectory of the particle will occur as the frame is being shrunk?

A particle of mass $m$ and charge $q$ moving with a velocity $\vec{v} = v_0(\hat{i} + \hat{j} - \hat{k})$ is placed in a uniform magnetic field $\vec{B} = B_0(\hat{i} + \hat{j} + \hat{k})$. It executes a helical trajectory of radius $r$ and pitch $p$. Which of the following options is correct?

Consider two waves, which are given by $y_1(x, t) = A \sin(kx - \omega t)$ and $y_2(x, t) = \sqrt{3}A \cos(kx - \omega t)$, where $k$ is the wave number and $\omega$ is the angular frequency. The amplitude of the resultant waveform obtained by the superposition of the two waves is $A_s$ and its phase difference with $y_1$ is $\phi_s$. What are $A_s$ and $\phi_s$?

A metallic cube initially kept at a temperature $T$ is emitting black body radiation with a power $P$ (energy emitted per unit time). If $T$ is increased by $1\%$, the power being radiated increases by $4.5\%$. What is the approximate percentage increase in the volume of the cube in this process?

A circular disk of mass $M$ and radius $R$ is rotating clockwise with a uniform angular velocity $\omega$ about an axis passing through the centre, normal to the disk. At time $t = 0$, a torque $T$ is applied along the same axis to oppose the rotation of the disk. What is the angular displacement $\theta$ (measured from $t = 0$ in the clockwise direction) that the disk attains before it starts rotating counterclockwise?

A particle of charge $q = 1e$ and mass $m$ with kinetic energy $K$ enters an electric field set up by two parallel plates of length $l$ as illustrated in the figure. The potential difference between the two plates is $1\text{ V}$ and their separation is $d$. What is the minimum value of $K$ (in $\text{eV}$) for which the particle will not hit either of the plates? [$e$ is the charge of the electron.]}