JEE Main 2010 Physics Paper: AIEEE

In the circuit shown below, the key $K$ is closed at $t = 0.$ The current through the battery is

In a series $LCR$ circuit $R = 200\ \Omega$ and the voltage and the frequency of the main supply are $220\text{ V}$ and $50\text{ Hz}$ respectively. On taking out the capacitance from the circuit the current lags behind the voltage by $30^\circ.$ On taking out the inductor from the circuit the current leads the voltage by $30^\circ.$ The power dissipated in the $LCR$ circuit is

Let $C$ be the capacitance of a capacitor discharging through a resistor $R.$ Suppose $t_1$ is the time taken for the energy stored in the capacitor to reduce to half its initial value and $t_2$ is the time taken for the charge to reduce to one-fourth its initial value. Then the ratio $t_1/t_2$ will be

For a particle in uniform circular motion the acceleration$\vec{a}$at a point P(R, θ) on the circle of radius R is (here θ is measured from the x–axis)

A point $P$ moves in counter-clockwise direction on a circular path as shown in the figure. The movement of $P$ is such that it sweeps out a length $s = t^3 + 5,$ where $s$ is in metres and $t$ is in seconds. The radius of the path is $20\text{ m}.$ The acceleration of $'P'$ when $t = 2\text{ s}$ is nearly.

Two conductors have the same resistance at $0^\circ\text{C}$ but their temperature coefficients of resistance are $\alpha_1$ and $\alpha_2.$ The respective temperature coefficients of their series and parallel combinations are nearly

Statement - $1$: When ultraviolet light is incident on a photocell, its stopping potential is $V_0$ and the maximum kinetic energy of the photoelectrons is $K_\mathrm{max}$. When the ultraviolet light is replaced by $X$-rays, both $V_0$ and $K_\mathrm{max}$ increase.

Statement - $2$: Photoelectrons are emitted with speeds ranging from zero to a maximum value because of the range of frequencies present in the incident light.

If a source of power $4\text{ kW}$ produces $10^{20}$ photons/second, the radiation belongs to a part of the spectrum called

A rectangular loop has a sliding connector $PQ$ of length $l$ and resistance $R\,\Omega$ and it is moving with a speed $v$ as shown. The set-up is placed in a uniform magnetic field going into the plane of the paper. The three currents $I_1, I_2$ and $I$ are

Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of $30^\circ$ with each other. When suspended in a liquid of density $0.8\text{ g cm}^{-3},$ the angle remains the same. If density of the material of the sphere is $1.6\text{ g cm}^{-3},$ the dielectric constant of the liquid is

A thin semi-circular ring of radius $r$ has a positive charges $q$ distributed uniformly over it. The net field $\vec{E}$ at the center $O$ is

Let there be a spherically symmetric charge distribution with charge density varying as $\rho(r) = \rho_0\left(\frac{5}{4} - \frac{r}{R}\right)$ upto $r = R,$ and $\rho(r) = 0$ for $r > R,$ where $r$ is the distance from the origin. The electric field at a distance $r\ (r < R)$ from the origin is given by

A ball is made of a material of density $\rho$ where $\rho_{oil} < \rho < \rho_{water}$ with $\rho_{oil}$ and $\rho_{water}$ representing the densities of oil and water, respectively. The oil and water are immiscible. If the above ball is in equilibrium in a mixture of this oil and water, which of the following pictures represents its equilibrium position?

Two fixed frictionless inclined planes making an angle $30^\circ$ and $60^\circ$ with the vertical are shown in the figure. Two blocks $A$ and $B$ are placed on the two planes. What is the relative vertical acceleration of $A$ with respect to $B$?

Two long parallel wires are at a distance $2d$ apart. They carry steady equal currents flowing out of the plane of the paper as shown. The variation of the magnetic field $B$ along the line $XX'$ is given by

A nucleus of mass $M + \Delta m$ is at rest and decays into two daughter nuclei of equal mass $\frac{M}{2}$ each. Speed of light is $c.$

The binding energy per nucleon for the parent nucleus is $E_{1}$ and that for the daughter nuclei is $E_{2}.$ Then

A nucleus of mass $M + \Delta m$ is at rest and decays into two daughter nuclei of equal mass $\frac{M}{2}$ each. Speed of light is $c.$

The speed of daughter nuclei is

A radioactive nucleus (initial mass number $A$ and atomic number $Z$ emits $3\alpha$- particles and $2$ positrons. The ratio of number of neutrons to that of protons in the final nucleus will be

A particle is moving with velocity$\vec{v} = k\left(y\hat{i} + x\hat{j}\right)$, where K is a constant. The general equation for its path is

An initially parallel cylindrical beam travels in a medium of refractive index $\mu(I) = \mu_0 + \mu_2 I,$ where $\mu_0$ and $\mu_2$ are positive constants and $I$ is the intensity of the light beam. The intensity of the beam is decreasing with increasing radius.

As the beam enters the medium, it will

An initially parallel cylindrical beam travels in a medium of refractive index $\mu(I) = \mu_0 + \mu_2 I,$ where $\mu_0$ and $\mu_2$ are positive constants and $I$ is the intensity of the light beam. The intensity of the beam is decreasing with increasing radius.

The speed of light in the medium is

A small particle of mass $m$ is projected at an angle $\theta$ with the $x$-axis with an initial velocity $v_0$ in the $x\text{-}y$ plane as shown in the figure. At a time $t < \frac{v_0\sin\theta}{g},$ the angular momentum of the particle is ................,

where $\hat{i}, \hat{j}$ and $\hat{k}$ are unit vectors along $x, y$ and $z$-axis respectively.

The combination of gates shown below yields

A diatomic ideal gas is used in a Carnot engine as the working substance. If during the adiabatic expansion part of the cycle the volume of the gas increases from $V$ to $32\ V$, the efficiency of the engine is

The respective number of significant figures for the numbers 23.023, 0.0003 and 2.1 $\times$ 10–3 are

The equation of a wave on a string of linear mass density $0.04\text{ kg m}^{-1}$ is given by $y = 0.02\,(\text{m})\sin\left[2\pi\left(\frac{t}{0.04\,(\text{s})} - \frac{x}{0.50\,(\text{m})}\right)\right].$

The tension in the string is

An initially parallel cylindrical beam travels in a medium of refractive index $\mu(I) = \mu_0 + \mu_2 I,$ where $\mu_0$ and $\mu_2$ are positive constants and $I$ is the intensity of the light beam. The intensity of the beam is decreasing with increasing radius.

The initial shape of the wavefront of the beam is

The potential energy function for the force between two atoms in a diatomic molecule is approximately given by $U(x) = \frac{a}{x^{12}} - \frac{b}{x^6},$ where $a$ and $b$ are constants and $x$ is the distance between the atoms. If the dissociation energy of the molecule is

$D = \left[U(x = \infty) - U_{at\ equilibrium}\right], \quad D$ is