JEE Main 2023 Physics Paper: 1 Feb, Shift 2

A square shaped coil of area $70\text{ cm}^2$ having 600 turns rotates in a magnetic field of $0.4\text{ wbm}^{-2}$, about an axis which is parallel to one of the sides of the coil and perpendicular to the direction of field. If the coil completes 500 revolutions in a minute, the instantaneous emf when the plane of the coil is inclined at $60^\circ$ with the field, will be ____________ V. (Take $\pi = \frac{22}{7}$)

An electron of a hydrogen like atom, having $Z = 4$, jumps from $4$th energy state to $2$nd energy state. The energy released in this process, will be:

(Given Rch = $13.6\text{ eV}$)

Where R = Rydberg constant

c = Speed of light in vacuum

h = Planck's constant

Given below are two statements: One is labeled as Assertion A and the other is labeled as Reason R.

Assertion A: Two metallic spheres are charged to the same potential. One of them is hollow and another is solid, and both have the same radii. Solid sphere will have lower charge than the hollow one.

Reason R: Capacitance of metallic spheres depends on the radii of spheres

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

Equivalent resistance between the adjacent corners of a regular n-sided polygon of uniform wire of resistance R would be:

In the given circuit, the value of $\left|\frac{I_1+I_3}{I_2}\right|$ is _____________

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

Assertion A: For measuring the potential difference across a resistance of $600\ \Omega$, the voltmeter with resistance $1000\ \Omega$ will be preferred over voltmeter with resistance $4000\ \Omega$.

Reason R: Voltmeter with higher resistance will draw smaller current than voltmeter with lower resistance.

In the light of the above statements, choose the most appropriate answer from the options given below.

The threshold frequency of a metal is $f_0$. When the light of frequency $2f_0$ is incident on the metal plate, the maximum velocity of photoelectrons is $v_1$. When the frequency of incident radiation is increased to $5f_0$, the maximum velocity of photoelectrons emitted is $v_2$. The ratio of $v_1$ to $v_2$ is:

A coil is placed in magnetic field such that plane of coil is perpendicular to the direction of magnetic field. The magnetic flux through a coil can be changed:

A. By changing the magnitude of the magnetic field within the coil.

B. By changing the area of coil within the magnetic field.

C. By changing the angle between the direction of magnetic field and the plane of the coil. D. By reversing the magnetic field direction abruptly without changing its magnitude. Choose the most appropriate answer from the options given below:

The ratio of average electric energy density and total average energy density of electromagnetic wave is:

A cubical volume is bounded by the surfaces $x = 0, x = a, y = 0, y = a, z = 0, z = a$. The electric field in the region is given by $\vec{E} = E_0 x\hat{i}$. Where $E_0 = 4 \times 10^{4}\text{ NC}^{-1}\text{ m}^{-1}$. If $a = 2\text{ cm}$, the charge contained in the cubical volume is $Q \times 10^{-14}\text{ C}$. The value of $Q$ is ________________. (Take $\epsilon_0 = 9 \times 10^{-12}\text{ C}^{2}/\text{Nm}^{2}$)

The surface of water in a water tank of cross section area $750\text{ cm}^2$ on the top of a house is $h\text{ m}$ above the tap level. The speed of water coming out through the tap of cross section area $500\text{ mm}^2$ is $30\text{ cm/s}$. At that instant, $\frac{dh}{dt}$ is $x \times 10^{-3}\text{ m/s}$. The value of $x$ will be ____________.

The escape velocities of two planets $\text{A}$ and $\text{B}$ are in the ratio $1 : 2$. If the ratio of their radii respectively is $1 : 3$, then the ratio of acceleration due to gravity of planet A to the acceleration of gravity of planet B will be:

As shown in the figure a block of mass 10 kg lying on a horizontal surface is pulled by a force F acting at an angle $30^\circ$, with horizontal. For $\mu_s = 0.25$, the block will just start to move for the value of F: [Given $g = 10\text{ ms}^{-2}$ ]

Figures (a), (b), (c) and (d) show variation of force with time.

The impulse is highest in figure.

The Young's modulus of a steel wire of length $6\text{ m}$ and cross-sectional area $3\text{ mm}^2$, is $2 \times 10^{11}\text{ N/m}^2$. The wire is suspended from its support on a given planet. A block of mass $4\text{ kg}$ is attached to the free end of the wire. The acceleration due to gravity on the planet is $\frac{1}{4}$ of its value on the earth. The elongation of wire is (Take $g$ on the earth $= 10\text{ m/s}^2$):

For a train engine moving with speed of $20\text{ ms}^{-1}$, the driver must apply brakes at a distance of 500 $\text{m}$ before the station for the train to come to rest at the station. If the brakes were applied at half of this distance, the train engine would cross the station with speed $\sqrt{x}\text{ ms}^{-1}$. The value of $x$ is ____________.

(Assuming same retardation is produced by brakes)

As shown in the figure, a long straight conductor with semicircular arc of radius $\frac{\pi}{10}$ m is carrying current $I = 3\text{ A}$. The magnitude of the magnetic field, at the center O of the arc is: (The permeability of the vacuum $= 4\pi \times 10^{-7}\text{ NA}^{-2}$)

Nucleus A having $Z = 17$ and equal number of protons and neutrons has $1.2\text{ MeV}$ binding energy per nucleon.

Another nucleus $\text{B}$ of $Z = 12$ has total 26 nucleons and $1.8\text{ MeV}$ binding energy per nucleons. The difference of binding energy of $\text{B}$ and $\text{A}$ will be _____________ $\text{MeV}$.

Choose the correct length (L) versus square of the time period ($T^2$) graph for a simple pendulum executing simple harmonic motion.

For a body projected at an angle with the horizontal from the ground, choose the correct statement.

Two objects A and B are placed at 15 cm and 25 cm from the pole in front of a concave mirror having radius of curvature 40 cm. The distance between images formed by the mirror is _______________.

Moment of inertia of a disc of mass '$M$' and radius '$R$' about any of its diameter is $\frac{MR^2}{4}$. The moment of inertia of this disc about an axis normal to the disc and passing through a point on its edge will be, $\frac{x}{2}$ MR$2$. The value of $x$ is ___________.

Choose the correct statement about Zener diode:

For three low density gases A, B, C pressure versus temperature graphs are plotted while keeping them at constant volume, as shown in the figure.

The temperature corresponding to the point '$\text{K}$' is:

A Carnot engine operating between two reservoirs has efficiency $\frac{1}{3}$. When the temperature of cold reservoir is raised by x, its efficiency decreases to $\frac{1}{6}$. The value of x, if the temperature of hot reservoir is $99^\circ$ C, will be:

If the velocity of light $\mathrm{c}$, universal gravitational constant $\mathrm{G}$ and Planck's constant $\mathrm{h}$ are chosen as fundamental quantities. The dimensions of mass in the new system is:

As shown in the figure, in Young's double slit experiment, a thin plate of thickness $t = 10\ \mu\text{m}$ and refractive index $\mu = 1.2$ is inserted in front of slit $S_1$. The experiment is conducted in air $(\mu = 1)$ and uses a monochromatic light of wavelength $\lambda = 500\text{ nm}$. Due to the insertion of the plate, central maxima is shifted by a distance of $x\beta_0.\ \beta_0$ is the fringe-width before the insertion of the plate. The value of the $x$ is _____________.

A block is fastened to a horizontal spring. The block is pulled to a distance $x = 10\text{ cm}$ from its equilibrium position (at $x = 0$) on a frictionless surface from rest. The energy of the block at $x = 5\text{ cm}$ is $0.25\text{ J}$. The spring constant of the spring is ___________ $\text{Nm}^{-1}$

A force $F = \left(5 + 3y^2\right)$ acts on a particle in the $y$-direction, where $F$ is in newton and $y$ is in meter. The work done by the force during a displacement from $y = 2\text{ m}$ to $y = 5\text{ m}$ is ___________ J.