JEE Main 2009 Physics Paper: AIEEE

An inductor of inductance $L = 400\text{ mH}$ and resistors of resistance $R_1 = 2\ \Omega$ and $R_2 = 2\ \Omega$ are connected to a battery of $\text{emf } 12\text{ V}$ as shown in the figure. The internal resistance of the battery is negligible. The switch $S$ is closed at $t = 0.$ The potential drop across $L$ as a function of time is:

The transition from the state $n = 4$ to $n = 3$ in a hydrogen like atom results in ultraviolet radiation. Infrared radiation will be obtained in the transition from:

Statement - 1: The temperature dependence of resistance is usually given as $R = R_0(1 + \alpha\Delta t).$ The resistance of wire changes from $100\ \Omega$ to $150\ \Omega$ when its temperature is increased from $27^\circ\text{C}$ to $227^\circ\text{C}$. This implies that $\alpha = 2.5 \times 10^{-3}/\text{C}.$

Statement - 2: $R = R_0(1 + \alpha\Delta t)$ is valid only when the change in the temperature $\Delta T$ is small and $\Delta R = (R - R_0) \ll R_0.$

The surface of a metal is illuminated with the light of $400\text{ nm.}$ The kinetic energy of the ejected photoelectrons was found to be $1.68\text{ eV.}$ The work function of the metal is: $(hc = 1240\text{ eV.nm})$

A charge $Q$ is placed at each of the opposite corners of a square. A charge $q$ is placed at each of the other two corners. If the net electrical force on $Q$ is zero, then $Q/q$ equals:

(This question contains Statement-1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements.)

Statement-1: For a charged particle moving from point $P$ to point $Q$, the net work done by an electrostatic field on the particle is independent of the path connecting point $P$ to point $Q.$ Statement-2: The net work done by a conservative force on an object moving along a closed loop is zero.

Let $\rho(r) = \frac{Q}{\pi R^{4}}r$ be the charge density distribution for a solid sphere of radius $R$ and total charge $Q$. For a point $p$ inside the sphere at distance $r_1$ from the center of the sphere, the magnitude of electric field is:

Two points $P$ and $Q$ are maintained at the potentials of $10\text{ V}$ and $-4\text{ V}$, respectively. The work done in moving $100$ electrons from $P$ to $Q$ is:

The height at which the acceleration due to gravity becomes $\frac{g}{9}$ (where $g =$ the acceleration due to gravity on the surface of the earth) in terms of $R,$ the radius of the earth, is:

A long metallic bar is carrying heat from one of its ends to the other end under steady-state. The variation of temperature $\theta$ along the length $x$ of the bar from its hot end is best described by which of the following figures?

Two wires are made of the same material and have the same volume. However wire $1$ has cross- sectional area $A$ and wire $2$ has cross-sectional area $3A.$ If the length of wire $1$ increases by $\Delta x$ on applying force $F,$ how much force is needed to stretch wire $2$ by the same amount?

Consider a rubber ball freely falling from a height $h = 4.9\text{ m}$ onto a horizontal elastic plate. Assume that the duration of collision is negligible and the collision with the plate is totally elastic. Then the velocity as a function of time and the height as a function of time will be:

A current loop $ABCD$ is held fixed on the plane of the paper as shown in the figure. The arcs $BC$ (radius $= b$) and $DA$ (radius $= a$) of the loop are joined by two straight wires $AB$ and $CD$. A steady current $I$ is flowing in the loop. Angle made by $AB$ and $CD$ at the origin $O$ is $30^\circ.$ Another straight thin wire steady current $I_1$ flowing out of the plane of the paper is kept at the origin.

The magnitude of the magnetic field $(B)$ due to the loop $ABCD$ at the origin $(O)$ is:

A current loop $ABCD$ is held fixed on the plane of the paper as shown in the figure. The arcs $BC$ (radius $= b$) and $DA$ (radius $= a$) of the loop are joined by two straight wires $AB$ and $CD$. A steady current $I$ is flowing in the loop. Angle made by $AB$ and $CD$ at the origin $O$ is $30^\circ.$ Another straight thin wire steady current $I_1$ flowing out of the plane of the paper is kept at the origin.

Due to the presence of the current $I_1$ at the origin:

The above is a plot of binding energy per nucleon $E_b,$ against the nuclear mass $M; A, B, C, D, E, F$ correspond to different nuclei. Consider four reactions:

$(i)\ \ A + B \rightarrow C + \varepsilon \quad (ii)\ \ C \rightarrow A + B + \varepsilon$

$(iii)\ \ D + E \rightarrow F + \varepsilon \quad (iv)\ \ F \rightarrow D + E + \varepsilon,$

where $\varepsilon$ is the energy released? In which reactions is $\varepsilon$ positive?

If $x, v$ and $a$ denote the displacement, the velocity and the acceleration of a particle executing simple harmonic motion of time period $T,$ then, which of the following does not change with time?

A particle has an initial velocity $3\hat{i} + 4\hat{j}$ and an acceleration of $0.4\hat{i} + 0.3\hat{j}$. Its speed after 10 s is:

In an optics experiment, with the position of the object fixed, a student varies the position of a convex lens and for each position, the screen is adjusted to get a clear image of the object. A graph between the object distance $u$ and the image distance $v,$ from the lens, is plotted using the same scale for the two axes. A straight line passing through the origin and making an angle of $45^\circ$ with the $x$-axis meets the experimental curve at $P.$ The coordinates of $P$ will be:

A transparent solid cylindrical rod has a refractive index of $\frac{2}{\sqrt{3}}.$ It is surrounded by air. A light ray is incident at the mid-point of one end of the rod as shown in the figure.

The incident angle $\theta$ for which the light ray grazes along the wall of the rod is:

A thin uniform rod of length $l$ and mass $m$ is swinging freely about a horizontal axis passing through its end. Its maximum angular speed is $\omega$. Its center of mass rises to a maximum height of:

The logic circuit shown below has the input waveforms $\text{'}A\text{'}$ and $\text{'}B\text{'}$ as shown. Pick out the correct output waveform.

Output is

A $p\text{-}n$ junction $(D)$ shown in the figure can act as a rectifier. An alternating current source $(V)$ is connected in the circuit.

The current $(I)$ in the resistor $(R)$ can be shown by:

One $\text{kg}$ of a diatomic gas is at a pressure of $8 \times 10^{4}\text{ N/m}^{2}.$ The density of the gas is $4\text{ kg/m}^{3}$. What is the energy of the gas due to its thermal motion?

Two moles of helium gas are taken over the cycle $ABCD,$ as shown in the $P\text{-}T$ diagram.

Assuming the gas to be ideal the work done on the gas in taking it from $A$ to $B$ is:

Two moles of helium gas are taken over the cycle $ABCD,$ as shown in the $P\text{-}T$ diagram.

The work done on the gas in taking it from $D$ to $A$ is:

Two moles of helium gas are taken over the cycle $ABCD$, as shown in the $P\text{-}T$ diagram.

The net work done on the gas in the cycle $ABCDA$ is:

In an experiment the angles are required to be measured using an instrument, 29 divisions of the main scale exactly coincide with the 30 divisions of the vernier scale. If the smallest division of the main scale is half-a degree(=$0.5^\circ$), then the least count of the instrument is:

Three sound waves of equal amplitudes have frequencies $(v-1),\ v,\ (v+1).$ They superpose to give beats. The number of beats produced per second will be:

A motor cycle starts from rest and accelerates along a straight path at $2\text{ m/s}^2.$ At the starting point of the motor cycle there is a stationary electric siren. How far has the motor cycle gone when the driver hears the frequency of the siren at $94\%$ of its value when the motor cycle was at rest? (Speed of sound $= 330\text{ ms}^{-1}$)

A mixture of light, consisting of wavelength $590\text{ nm}$ and an unknown wavelength, illuminates Young's double slit and gives rise to two overlapping interference patterns on the screen. The central maximum of both lights coincide. Further, it is observed that the third bright fringe of known light coincides with the $4$th bright fringe of the unknown light. From this data, the wavelength of the unknown light is: