IAT (IISER) 2024

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 $L$, respective...

Atomic masses of two oxygen isotopes ${ }_8^{16} \mathrm{O}$ and ${ }_8^{18} \mathrm{O}$ are 15.99491 u and 17.99916 u , respectively, where $u$ is the atomic mass unit. Masses of protom and neutron are given by 1.00727 u and I .00866 u , r...

Consider the shown circuit. The capacitors $C_1$ and $C_2$ have capacitances $2 \mu \mathrm{~F}$ and $8 \mu \mathrm{~F}$, respectively. The switch can connect point $X$ to either $Y$ or $Z$. Initially $X Y$ is connected until the capacitor ...

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...

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 V and 3 V , respectively. What is the work function of the mate...

Consider two point charges $+q$ and $+2 q$ 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 $(0,(\sqrt{3} / 2) \ell)$ on the $x y$ plane, as sho...

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 l...

Two identical boxes contain the same ideal gas. Let $\left(n_1, \lambda_1, T_1\right)$ and $\left(n_2, \lambda_2, T_2\right)$ be the number density, mean free path and temperature of the gas in the first and the second box, respectively. On...

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

A conducting wire carrying a steady current $I$ is shaped as shown in the figure below. All connected graight 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 $...

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. Tw...

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 gr...

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 behaviour with an ampli...

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