JEE Main 2023 Physics Paper: 30 Jan, Shift 2

In an ac generator, a rectangular coil of 100 turns each having area $14 \times 10^{-2}\text{ m}^2$ is rotated at $360\text{ rev/min}$ about an axis perpendicular to a uniform magnetic field of magnitude $3.0\text{ T}$. The maximum value of the emf produced will be ________ $V$.

$($ Take $\pi = \frac{22}{7})$

In the given circuit, rms value of current $(I_{\text{rms}})$ through the resistor $R$ is:

A stone tied to $180\text{ cm}$ long string at its end is making 28 revolutions in horizontal circle in every minute. The magnitude of acceleration of stone is $\frac{1936}{x}\text{ m s}^{-2}$. The value of $x$ ________. (Take $\pi = \frac{22}{7}$)

The equivalent resistance between $A$ and $B$ is _________.

If the potential difference between $\mathrm{B}$ and $\mathrm{D}$ is zero, the value of $x$ is $\frac{1}{n}\ \Omega$. The value of $n$ is __________.

An electron accelerated through a potential difference $V_1$ has a de-Broglie wavelength of $\lambda$. When the potential is changed to $V_2$, its de-Broglie wavelength increases by $50\%$. The value of $\left(\frac{V_1}{V_2}\right)$ is equal to

A point source of $100\text{ W}$ emits light with $5\%$ efficiency. At a distance of $5\text{ m}$ from the source, the intensity produced by the electric field component is:

As shown in the figure, a point charge $Q$ is placed at the centre of conducting spherical shell of inner radius $a$ and outer radius $b$. The electric field due to charge $Q$ in three different regions $\text{I, II}$ and $\text{III}$ is given by:

$(\text{I}: r < a, \text{II}: a < r < b$, III: $r > b$)

As shown in figure, a cuboid lies in a region with electric field $E = 2x^{2}\hat{i} - 4y\hat{j} + 6\hat{k}\text{ N/C}$. The magnitude of charge within the cuboid is $n\epsilon_0\text{ C}$.

The value of $n$ is _________ (if dimension of cuboid is $1 \times 2 \times 3\text{ m}^{3}$)

An object is allowed to fall from a height $R$ above the earth, where $R$ is the radius of earth. Its velocity when it strikes the earth's surface, ignoring air resistance, will be

A flask contains hydrogen and oxygen in the ratio of $2 : 1$ by mass at temperature $27^\circ\text{C}$. The ratio of average kinetic energy per molecule of hydrogen and oxygen respectively is:

A block of $\sqrt{3}\text{ kg}$ is attached to a string whose other end is attached to the wall. An unknown force $F$ is applied so that the string makes an angle of $30^\circ$ with the wall. The tension $T$ is: (Given $g = 10\text{ m s}^{-2}$)

A force is applied to a steel wire 'A', rigidly clamped at one end. As a result elongation in the wire is $0.2\text{ mm}$. If same force is applied to another steel wire ' $B$ ' of double the length and a diameter $2.4$ times that of the wire ' $A$ ', the elongation in the wire ' $B$ ' will be (wires having uniform circular cross sections)

A vehicle travels $4\text{ km}$ with speed of $3\text{ km/h}$ and another $4\text{ km}$ with speed of $5\text{ km/h}$, then its average speed is

A current carrying rectangular loop PQRS is made of uniform wire. The length $PR = QS = 5\text{ cm}$ and $PQ = RS = 100\text{ cm}$. If ammeter current reading changes from I to $2I$, the ratio of magnetic forces per unit length on the wire $PQ$ due to wire $RS$ in the two cases respectively $\left(f_{PQ}^{I} : f_{PQ}^{2I}\right)$ is:

As shown in the figure, a current of $2\text{ A}$ flowing in an equilateral triangle of side $4\sqrt{3}\text{ cm}$. The magnetic field at the centroid $\text{O}$ of the triangle is

(Neglect the effect of earth's magnetic field)

A radioactive nucleus decays by two different processes. The half life of the first process is 5 minutes and that of the second process is $30\text{ s}$. The effective half-life of the nucleus is calculated to be $\frac{\alpha}{11}\text{ s}$. The value of $\alpha$ is __________.

Given below are two statements: one is labelled as Assertion $\mathbf{A}$ and the other is labelled as Reason $\mathbf{R}$

Assertion A: The nuclear density of nuclides ${}_{5}^{10}\text{B}, {}_{3}^{6}\text{Li}, {}_{26}^{56}\text{Fe}, {}_{10}^{20}\text{Ne}$ and ${}_{83}^{209}\text{Bi}$ can be arranged as $\rho_{\text{Bi}}^{\text{N}} > \rho_{\text{Fe}}^{\text{N}} > \rho_{\text{Ne}}^{\text{N}} > \rho_{\text{B}}^{\text{N}} > \rho_{\text{Li}}^{\text{N}}$

Reason R: The radius $R$ of nucleus is related to its mass number $A$ as $R = R_0 A^{1/3}$, where $R_0$ is a constant.

In the light of the above statements, choose the correct answer from the options given below

For a simple harmonic motion in a mass spring system shown, the surface is frictionless. When the mass of the block is $1\text{ kg}$, the angular frequency is $\omega_1$. When the mass block is $2\text{ kg}$ the angular frequency is $\omega_2$. The ratio $\omega_2/\omega_1$ is

The velocity of a particle executing SHM varies with displacement $(x)$ as $4v^2 = 50 - x^2$. The time period of oscillations is $\frac{x}{7}\text{ s}$. The value of $x$ is ___________. $($ Take $\pi = \frac{22}{7})$

A thin prism $P_1$ with an angle $6^\circ$ and made of glass of refractive index $1.54$ is combined with another prism $P_2$ made from glass of refractive index $1.72$ to produce dispersion without average deviation. The angle of prism $P_2$ is

A uniform disc of mass $0.5\text{ kg}$ and radius $r$ is projected with velocity $18\text{ m/s}$ at $t = 0$ s on a rough horizontal surface. It starts off with a purely sliding motion at $t = 0\text{ s}$. After $2\text{ s}$ it acquires a purely rolling motion (see figure). The total kinetic energy of the disc after $2\text{ s}$ will be __________ $\text{J}$ (given, coefficient of friction is $0.3$ and $g = 10\text{ m/s}^{2}$ ).

The output $Y$ for the inputs $A$ and $B$ of circuit is given by

Truth table of the shown circuit is:

Given below are two statements: one is labelled as Assertion $\mathbf{A}$ and the other is labelled as Reason $\mathbf{R}$

Assertion A: Efficiency of a reversible heat engine will be highest at $-273^\circ\text{C}$ temperature of cold reservoir.

Reason R: The efficiency of Carnot's engine depends not only on the temperature of the cold reservoir but it depends on the temperature of the hot reservoir too and is given as $\eta = \left(1 - \frac{T_2}{T_1}\right)$ In the light of the above statements, choose the correct answer from the options given below

A faulty thermometer reads $5^\circ\text{C}$ in melting ice and $95^\circ\text{C}$ in steam. The correct temperature on absolute scale will be __________ $\text{K}$ when the faulty thermometer reads $41^\circ\text{C}$.

Match List I with List II:

Choose the correct answer from the options given below:

In a Young's double slit experiment, the intensities at two points, for the path differences $\frac{\lambda}{4}$ and $\frac{\lambda}{3}$ ( $\lambda$ being the wavelength of light used) are $I_1$ and $I_2$ respectively. If $I_0$ denotes the intensity produced by each one of the individual slits, then $\frac{I_1+I_2}{I_0} =$ __________.

A body of mass $2\text{ kg}$ is initially at rest. It starts moving unidirectionally under the influence of a source of constant power P. Its displacement in $4\text{ s}$ is $\frac{1}{3}\alpha^2\sqrt{P}\text{ m}$. The value of $\alpha$ will be ______.