JEE Main 2012 Physics Paper: AIEEE

A diatomic molecule is made of two masses $m_1$ and $m_2$ which are separated by a distance $r.$ If we calculate its rotational energy by applying Bohr's rule of angular momentum quantization, its energy will be given by: ($n$ is an integer)

Hydrogen atom is excited from ground state to another state with principal quantum number equal to $4.$ Then the number of spectral lines in the emission spectra will be:

The figure shows an experimental plot for discharging of a capacitor in an R-C circuit. The time constant $\tau$ of this circuit lies between

Two cars of masses m1 and m2 are moving in circles of radii r1 and r2, respectively. Their speeds are such that they make complete circles in the same time t. The ratio of their centripetal acceleration is

Two electric bulbs marked $25\text{ W} - 220\text{ V}$ and $100\text{ W} - 220\text{ V}$ are connected in series to a $440\text{ V}$ supply. Which of the bulbs will fuse?

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

Statement 1: Davisson - Germer experiment established the wave nature of electrons. Statement 2: If electrons have wave nature, they can interfere and show diffraction.

A coil is suspended in a uniform magnetic field, with the plane of the coil parallel to the magnetic lines of force. When a current is passed through the coil it starts oscillating; It is very difficult to stop. But if an aluminium plate is placed near to the coil, it stops. This is due to:

An electromagnetic wave in vacuum has the electric and magnetic field $\vec{E}$and $\vec{B}$, which are always perpendicular to each other. The direction of polarization is given by $\vec{X}$ and that of wave propagation by$\vec{k}$. Then

In a uniformly charged sphere of total charge $Q$ and radius $R,$ the electric field $E$ is plotted as a function of distance from the center. The graph which would correspond to the above will be:

This question has statement- $1$ and statement- $2.$ Of the four choices given after the statements, choose the one that best describes the two statements.

An insulating solid sphere of radius $R$ has a uniformly positive charge density $\rho$. As a result of this uniform charge distribution there is a finite value of electric potential at the center of the sphere, at the surface of the sphere and also at a point outside the sphere. The electric potential at infinity is zero.

Statement- $1:$ When a charge $q$ is taken from the centre to the surface of the sphere its potential energy changes by $\frac{q\rho}{3\varepsilon_0}$

Statement- $2:$ The electric field at a distance $r\,(r < R)$ from the center of the sphere is $\frac{\rho r}{3\varepsilon_0}$

The mass of a spaceship is $1000\text{ kg}.$ It is to be launched from the earth's surface out into free space. The value of $g$ and $R$ (radius of earth) are $10\text{ m/s}^{2}$ and $6400\text{ km}$ respectively. The required energy for this work will be:

A particle of mass $m$ is at rest at the origin at time $t = 0$ It is subjected to a force $F(t) = F_0e^{-bt}$ in the $x$ direction. Its speed $v(t)$ is depicted by which of the following curves?

A charge $Q$ is uniformly distributed over the surface of non-conducting disc of radius $R.$ The disc rotates about an axis perpendicular to its plane and passing through its center with an angular velocity $\omega.$ As a result of this rotation a magnetic field of induction $B$ is obtained at the center of the disc. If we keep both the amount of charge placed on the disc and its angular velocity to be constant and vary the radius of the disc then the variation of the magnetic induction at the center of the disc will be represented by the figure:

Proton, deuteron and alpha particle of same kinetic energy are moving in circular trajectories in a constant magnetic field. The radii of proton, deuteron and alpha particle are respectively $r_p, r_d$ and $r_\alpha$. Which one of the following relations is correct?

Assume that a neutron breaks into a proton and an electron. The energy released during this process is: (mass of neutron $= 1.6725 \times 10^{-27}\text{ kg},$ mass of proton $= 1.6725 \times 10^{-27}\text{ kg},$ mass of electron $= 9 \times 10^{-31}\text{ kg}$ ).

If a simple pendulum has significant amplitude (up to a factor of $1/e$ of original) only in the period between $t = 0\text{ s to } t = \tau\text{ s},$ then $\tau$ may be called the average life of the pendulum When the spherical bob of the pendulum suffers a retardation (due to viscous drag) proportional to its velocity with $b$ as the constant of proportionality, the average life time of the pendulum is (assuming damping is small) in seconds:

A boy can throw a stone up to a maximum height of 10 m. The maximum horizontal distance that the boy can throw the same stone up to will be

An object $2.4\text{ m}$ in front of a lens forms a sharp image on a film $12\text{ cm}$ behind the lens. A glass plate $1\text{ cm}$ thick, of refractive index $1.50$ is interposed between lens and film with its plane faces parallel to film. At what distance (from lens) should object shifted to be in sharp focus of film?

Truth table for system of four $NAND$ gates as shown in figure is:

A thin liquid film formed between a U-shaped wire and a light slider supports a weight of $1.5 \times 10^{-2}\text{ N}$ (see figure). The length of the slider is $30\text{ cm}$ and its weight negligible. The surface tension of the liquid film is

A Carnot engine, whose efficiency is $40\%$, takes in heat from a source maintained at a temperature of $500\ K.$ It is desired to have an engine of efficiency $60\%.$ Then, the intake temperature for the same exhaust (sink) temperature must be:

Helium gas goes through a cycle $ABCD$ (consisting of two isochoric and isobaric lines) as shown in figure efficiency of this cycle is nearly: (Assume the gas to be close to ideal gas)

A wooden wheel of radius $R$ is made of two semicircular part (see figure). The two parts are held together by a ring made of a metal strip of cross sectional area $S$ and length $L.\ L$ is slightly less than $2\pi R.$ To fit the ring on the wheel, it is heated so that its temperature rises by $\Delta T$ and it just steps over the wheel. As it cools down to surrounding temperature, it process the semicircular parts together. If the coefficient of linear expansion of the metal is $\alpha$, and its Young's modulus is $Y,$ the force that one part of the wheel applies on the other part is:

Resistance of a given wire is obtained by measuring the current flowing in it and the voltage difference applied across it. If the percentage errors in the measurement of the current and the voltage difference are 3% each, then error in the value of resistance of the wire is

A spectrometer gives the following reading when used to measure the angle of a prism. Main scale reading: 58.5 degree

Vernier scale reading: 09 divisions

Given that 1 division on main scale corresponds to 0.5 degree. Total divisions on the vernier scale is 30 and match with 29 divisions of the main scale. The angle of the prism from the above data is

A cylindrical tube, open at both ends, has a fundamental frequency, $f,$ in air. The tube is dipped vertically in water so that half of it is in water. The fundamental frequency of the air-column is now:

In Young's double slit experiment, one of the slit is wider than other, so that amplitude of the light from one slit is double of that from other slit. If $I_m$ be the maximum intensity, the resultant intensity $I$ when they interfere at phase difference $\phi$ is given by:

This question has Statement $1$ and Statement $2.$ Of the four choices given after the Statements, choose the one that best describes the two Statements.

If two springs $S_1$ and $S_2$ of force constants $k_1$ and $k_2$, respectively, are stretched by the same force, it is found that more work is done on spring $S_1$ than on spring $S_2$.

STATEMENT 1: If stretched by the same amount, work done on $S_1$ is more than that on $S_2$ STATEMENT 2: $k_1 < k_2$