List of top Physics Questions asked in IISER

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?

Consider an elastic collision between two particles $A$ and $B$ of same mass, moving in the same direction. Particle $A$ is moving at speed $v_A$ and particle $B$ is moving at speed $v_B$. In the figures shown, the solid lines represent the motion before the collision and the dotted lines represent the motion after the collision. Which of the following describes the motion of these two particles most accurately?

A block of mass $M$ lies at rest connected to a massless spring of spring constant $k$ on a frictionless surface. A bullet of mass $m$ hits the block horizontally with speed $v$ as shown in the figure and is completely stuck to the block. What is the maximum compression in the spring resulting from this impact (assuming that at this point the spring is still not fully compressed)?

A cart of mass $M$ is released from $A$, the highest point of a frictionless track, as shown in the figure. The cart travels along the track and enters the semicircular arc $DBC$ of radius $R$. The heights of the points $A$ and $B$ are $h_1$ and $h_2$ from the ground, respectively. Which of the following quantities does not play any role in ensuring that the cart does not leave the track?

A conducting wire carrying a steady current \(I\) is shaped as shown in the figure below. All connected straight segments meet at right angles. What is the magnetic moment of the current loop?

The refractive indices (\(n\)) of two transparent slabs are \(2\) and \(2/\sqrt{3}\). They are attached together and placed in a third transparent medium of refractive index \(\sqrt{2}\), as shown in the figure. The thickness of the upper slab is \(1\ \text{cm}\). A monochromatic light ray is incident on the upper slab at \(45^\circ\). What would be the thickness in \(\text{cm}\) of the lower slab such that the lateral shift of the ray after passing through both the slabs is zero?

Atomic masses of two oxygen isotopes \(^{16}_{8}\text{O}\) and \(^{18}_{8}\text{O}\) are \(15.99491\ \text{u}\) and \(17.99916\ \text{u}\), respectively, where \(\text{u}\) is the atomic mass unit. Masses of proton and neutron are given by \(1.00727\ \text{u}\) and \(1.00866\ \text{u}\), respectively. The speed of light is \(c\). What is the difference between the binding energies of \(^{18}_{8}\text{O}\) and \(^{16}_{8}\text{O}\) nuclei in units of \(\text{u } c^2\)?

Two monochromatic sources emit light at wavelengths \(\lambda\) and \(\lambda/2\). The stopping potentials for a photosensitive material using these two sources are found to be \(1\ \text{V}\) and \(3\ \text{V}\), respectively. What is the work function of the material?

Consider the circuit diagram as shown in the figure. The source has a voltage \(V = V_0 \sin \omega t\). Both the resistors A and B have the same resistance. The capacitor and the inductor have capacitance \(C\) and inductance \(L\), respectively. For some frequency \(\omega\), and certain initial charge in the capacitor, the current through the resistor A is in phase with the source. What is the value of \(\omega\)?

Consider the circuit shown in the figure. The capacitors C1 and C2 have capacitances \(2\ \mu\text{F}\) and \(8\ \mu\text{F}\), respectively. The switch can connect point X to either Y or Z. Initially XY is connected until the capacitor is fully charged by the battery. Then the switch connects X and Z, and the final charges on C1 and C2 are \(Q_1\) and \(Q_2\), respectively. What is the value of the ratio \(\frac{Q_2}{Q_1 + Q_2}\)?

Consider a solid sphere of radius \(R\) floating in a pond with half of the sphere submerged. The sphere is pushed vertically downwards at the topmost point and released, such that it executes a simple harmonic motion. Acceleration due to gravity is \(g\). What is the time period of oscillation?

Consider the motion of a particle along the \(x\)-axis. The position of the particle varies with time \(t\) as \(x(t) = \sin^2(\omega t) \cos^3(\omega t)\), where \(\omega\) is a constant. What is the time period of the motion?

Consider two point charges \(+q\) and \(+2q\) fixed on the \(x-y\) plane at \((-\ell/2, 0)\) and \((+\ell/2, 0)\) respectively. Another point charge \(-q\) having mass \(m\) is released from rest at \((0, \frac{\sqrt{3}}{2}\ell)\) on the \(x-y\) plane, as shown in the figure. The permittivity of free space is \(\epsilon_0\). What is the acceleration of the charge \(-q\) at the time of release?

A solid bob of a material having density twice that of water is suspended with a massless and inextensible string of length \(L\). The whole set-up is placed inside a water-filled tank. The bob is imparted a horizontal velocity \(V_0\) at the lowest point \(A\), while the other end of the string is fixed, such that the bob completes a semi-circular trajectory in the vertical plane. The string becomes slack only when the bob reaches the topmost point \(C\). Assume that the effects of viscosity and water currents are negligible. The acceleration due to gravity is \(g\). What is the expression for \(V_0\)?

One mole of an ideal gas of volume \(V\) and temperature \(T\) is allowed to expand adiabatically to volume \(2V\) while doing no external work. The universal gas constant is \(R\). What is the pressure of the gas after expansion?

Two identical boxes contain the same ideal gas. Let \((n_1, \lambda_1, T_1)\) and \((n_2, \lambda_2, T_2)\) be the number density, mean free path and temperature of the gas in the first and the second box, respectively. One of the boxes is emptied into the other one. What will be the mean free path \(\lambda\) and temperature \(T\) of the gas now?

Consider a simple pendulum undergoing simple harmonic motion with a time period \(T\), and a fixed amplitude \(\theta_0\) of angular oscillation. Its angular momentum about the point of suspension exhibits an oscillatory behavior with an amplitude \(A\). Which of the following relations between \(A\) and \(T\) is correct?

On a circular track, two cyclists, Abhijit and Vani, start moving in opposite directions from a point. Abhijit moves with a constant speed. Vani starts with a constant acceleration from rest. They meet again on the track with the same speed. Which of the following is correct?

An inextensible cord of negligible mass passes over the rim of a solid disc of mass \(M\) and radius \(R\). The disc is free to rotate about an axis passing through the centre perpendicular to the plane of the screen, as shown in the figure. Two blocks of masses \(M\) and \(M/2\) are attached to the two free ends of the cord. Assume that there is no slipping of the cord on the disc. The acceleration due to gravity is \(g\). What is the value of the angular acceleration of the disc?