IAT (IISER) 2026

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 radi...

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 trav...

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 plan...

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 ...

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 to...

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 $F_1$ a...

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 ...

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{...

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 s...

The acceleration of a point particle is given by the equation$\dfrac{d^2\mathbf{x}}{dt^2} = \alpha \dfrac{\mathbf{x}}{|\mathbf{x}|^7} + \beta \dfrac{d\mathbf{x}}{dt}$where $\mathbf{x}$ denotes position and $t$ denotes time. Which of the fol...