IAT (IISER) 2022

Two uniformly charged concentric thin spherical shells of radii $r_1$ and $r_2$ have charges $+Q$ and $-Q$, respectively. How does the electrostatic potential vary with distance from the center of the shells?

A conducting sphere of radius $a$ initially contains a uniform volume charge density $\rho$. What is the electric flux $\Phi$ through a spherical surface of radius $2 a$ centered at a point on the surface of the charged sphere (see figure) ...

Consider a very long cylinder of radius $a$ having a uniform positive charge density $\rho$. A sphere of radius $a$ has been carved out (see figure), leaving no charge in that region. The distance radially outward to the cylinder, as measur...

A liquid of density $\rho$ in a container weighs $W$. A cubic block of side $L$ and density $\rho_b<\rho$ is pushed by a stick to completely submerge the block in the liquid without touching the bottom. If $g$ is the acceleration due to the...

A monoatomic ideal gas at pressure $P$ and volume $V$ is first adiabatically compressed to volume $V / 8$ and then is allowed to expand isothermally back to its original volume. What is the final pressure of the gas?

A particle experiences an acceleration $\vec{a}=\alpha \vec{v}$, where $\vec{v}$ is the velocity of the particle and $\alpha$ is a constant. If the distances traveled by the particle in the time intervals $t_2-t_1$ and $t_3-t_1$ are $S_{12}...

A thin lens made of material of refractive index $n_l$ forms the image at the position $I$ of a point object held at $O$ on the central axis of the lens, as is shown in the ray diagram below. Consider that the refractive index of the medium...

As shown in the figure a block is resting on a frictionless floor and is attached to the free end of a spring. The right edge of the block in equilibrium is at a distance $d$ from the wall. When the spring is compressed by a distance $d / 2...

A uniform taut string with two point charges $q$ and $-q$ attached to its ends passes over two massless pullies kept $L$ distance apart as shown in the fgure. If $f$ is the fundamental frequency of the part of the string over pullies, which...

An object is released from rest from the inner edge of a hemispherical bowl, and it falls under gravity. The coefficient of kinetic friction between the object and the bowl is $\mu$. If the object covers an angular displacement $\theta$ wit...