IAT (IISER) 2020

The charge distribution inside a sphere of radius $R=2 a / b$ is given by the volume charge density $\rho=a r^2-b r^3$, where $a$ and $b$ are constants and $r$ is the radial distance from the center of the sphere. At what distance from the...

The acceleration due to earth's gravity on a point particle at a height $h$ above the surface of the earth is denoted by $g_o(h)$ and at a depth $d$ below the surface of the earth is denoted by $g_i(d)$. Consider the earth to be a sphere of...

Two identical containers kept at the same temperature carry the same gas with different molecular mean free paths $l_1$ and $l_2$. The gas from the first container is completely transferred into the second at the same temperature. What is t...

An ideal rigid diatomic gas undergoes expansion at constant pressure when $\Delta Q$ heat is added to it. What is the ratio of the change in the internal energy $\Delta U$ to the heat supplied $\Delta Q$ ?

Consider a mass-pulley system as shown in the figure. There is a wedge of mass $M$ and equal wedge angles $\theta$ lying on a rigid horizontal table. The coefficient of friction between the wedge and the table is $\mu$. There are two blocks...

What is the maximum angle of incidence $\theta_i$ in the figure for which the ray would satisfy the condition for total internal reflection at the boundary of media of refractive indices $n_1$ and $n_2$, where $n_1>n_2$ ?+

Consider a solid rod of mass $m$ and uniform density resting against a vertical wall and horizontal floor as shown in the figure. The coefficients of friction of the rod with the wall and with the floor are given to be $\mu_1$ and $\mu_2$ r...

Consider the circuit with a Zener diode whose breakdown voltage $V_z=4 \mathrm{~V}$. What is the voltage $V_0$ if $V_i=20 \mathrm{~V}$ ?

The fundamental constants are given to be permittivity constant $\left(\epsilon_0\right)$, Planck's constant $(h)$, velocity of light $(c)$, Newton's constant $(G)$ and Boltzmann's constant $\left(k_B\right)$. Which of the following quantit...

The potential energy of a point particle of mass $m$ undergoing rectilinear motion along the $x$-axis is given by
\(V(x)=A x+B x^2\)
What is the maximum speed attained by the particle if it starts from rest at $x=\frac{A}{B}$ ?