IAT (IISER) 2023

Consider the Bohr model of an atom where an electron of charge $-e$ revolves around a nucleus of charge $+e$ in an orbit of radius $r$. The electron has an orbital angular momentum $2 h$. If the nucleus had charge $+2 e$, what would have be...

A current $I$ flows through a cylindrical cable of length $L$ and uniform cross-sectional area $A$. The power dissipated due to the current is $P_1$. The cable is cut into two equal halves. If the cross-sectional area and the current flowin...

\(\text { What is the effective resistance between } A \text { and } B \text { in the circuit shown below? }\)

The magnetic fux $\phi_B(t)$ through a coil at a time $t$ is given by $\phi_B(t)=\phi_0 \cos \omega t$, where $0 \leq$ $\omega t \leq \pi$ and $\phi_0$ is a non-zero constant. At what time is the magnitude of the induced emf a maximum?

Particle A with charge $Q$ and particle B with charge $2 Q$ are fixed at positions $\vec{r}_A$ and $\vec{r}_B$, respectively. The force on $A$ due to $B$ is $\vec{F}_{B A}$, and that on $B$ due to $A$ is $\vec{F}_{A B}$. Which of the follow...

Two cubes $A$ and $B$ of same dimensions are made of different materials with densities $\rho_A$ and $\rho_{\mathrm{B}}$, respectively. Cube A floats in water with a fraction $\eta$ of its volume immersed. When cube $B$ is placed on top of ...

Two spherical bodies A and B each of mass $M$ and radius $R$ are located such that their centers are apart by a distance of $4 R$ as shown in the figure. An object $C$ of mass $m$ is thrown from the surface of A directly towards the center ...

57. Consider a Carnot heat engine operating between a heat reservoir at temperature 600 K , and an external atmosphere at temperature 300 K . In one cycle, 1000 kJ of heat is extracted from the heat reservoir, and the associated work is inp...

The velocity $v(t)$ of a particle moving in one dimension is given by:
$$ v(t)= \begin{cases}\alpha t, & 0 \leq t \leq T / 3 \\ \alpha T / 3, & T / 3 \leq t \leq 2 T / 3 \\ \alpha(T-t), & 2 T / 3 \leq t \leq T\end{cases} $$
where $\alpha(\n...

A ball is thrown vertically upwards with an initial speed $u$ from a height $h$ above the ground. The ball eventually hits the ground with a speed $v$. The acceleration due to gravity is $g$ and air resistance is negligible. What is the ave...

An object is placed in front of a convex lens. A real inverted image of double its size is formed. When the object is moved closer to the lens by a distance $d$, the image shifts away from the lens by a distance $8 d$ from its previous posi...

The intrinsic electron and hole concentrations of a Si-based intrinsic semiconductor are $n_e^{(0)}$ and $n_h^{(0)}$, respectively. Upon doping with trivalent impurities the respective carrier concentrations become $n_e$ and $n_h$. Which of...

A quantity has been measured to have a value of 0.00230 in some units. How many significant figures does the measured value have?

Two fixed point particles, each of charge $+q$, are separated by a distance $2 L$. Another point charge $+q$ of mass $m$ is oscillating about its equilibrium position as indicated in the figure below. The time period of oscillation is given...

The frequency of the whistle of a train moving with a constant speed is observed by a stationary detector on the platform to be $v_1$. The frequency of the same whistle is detected to be $v_2$ inside another train moving on a parallel track...