JEE Main 2024 Physics Paper: 4 Apr, Shift 2

Match List I with List II

Choose the correct answer from the options given below:

According to Bohr's theory, the moment of momentum of an electron revolving in $4$th orbit of hydrogen atom is:

A parallel plate capacitor of capacitance $12.5\text{ pF}$ is charged by a battery connected between its plates to potential difference of $12.0\text{ V}$. The battery is now disconnected and a dielectric slab $(\epsilon_r = 6)$ is inserted between the plates. The change in its potential energy after inserting the dielectric slab is ________ $\times 10^{-12}\text{ J}$.

In a system two particles of masses $m_1 = 3\text{ kg}$ and $m_2 = 2\text{ kg}$ are placed at certain distance from each other. The particle of mass $m_1$ is moved towards the center of mass of the system through a distance $2\text{ cm}$. In order to keep the center of mass of the system at the original position, the particle of mass $m_2$ should move towards the center of mass by the distance _________ $\text{cm}$.

A cyclist starts from the point $P$ of a circular ground of radius $2\text{ km}$ and travels along its circumference to the point $S$. The displacement of a cyclist is:

An electric bulb rated $50\text{ W} - 200\text{ V}$ is connected across a $100\text{ V}$ supply. The power dissipation of the bulb is:

Two wires $A$ and $B$ are made up of the same material and have the same mass. Wire $A$ has radius of $2.0\text{ mm}$ and wire $B$ has radius of $4.0\text{ mm}$. The resistance of wire $B$ is $2\ \Omega$. The resistance of wire $A$ is ________ $\Omega$.

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

Assertion A: Number of photons increases with increase in frequency of light.

Reason R: Maximum kinetic energy of emitted electrons increases with the frequency of incident radiation.

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

A rod of length $60\text{ cm}$ rotates with a uniform angular velocity $20\text{ rad s}^{-1}$ about its perpendicular bisector, in a uniform magnetic field $0.5\text{ T}$. The direction of magnetic field is parallel to the axis of rotation. The potential difference between the two ends of the rod is _________ V.

Arrange the following in the ascending order of wavelength:

A. Gamma rays $(\lambda_1)$

B. $x$ - rays $(\lambda_2)$

C. Infrared waves $(\lambda_3)$

D. Microwaves $(\lambda_4)$

Choose the most appropriate answer from the options given below

A charge $q$ is placed at the center of one of the surfaces of a cube. The flux linked with the cube is:

Mercury is filled in a tube of radius $2\text{ cm}$ up to a height of $30\text{ cm}$. The force exerted by mercury on the bottom of the tube is _________ N.

(Given, atmospheric $= 10^{5}\text{ N m}^{-2},\ g = 10\text{ m s}^{-2},\ \pi = \frac{22}{7})$pressure, density of mercury

$= 1.36 \times 10^{4}\text{ kg m}^{-3}$

A $90\text{ kg}$ body placed at $2R$ distance from surface of earth experiences gravitational pull of: ($R =$ Radius of earth, $g = 10\text{ m s}^{-2}$)

Correct formula for height of a satellite from earth's surface is:

A $2\text{ kg}$ brick begins to slide over a surface which is inclined at an angle of $45^\circ$ with respect to horizontal axis. The co-efficient of static friction between their surfaces is:

The magnetic moment of a bar magnet is $0.5\text{ Am}^2$. It is suspended in a uniform magnetic field of $8 \times 10^{-2}\text{ T}$. The work done in rotating it from its most stable to most unstable position is:

A bus moving along a straight highway with speed of $72\text{ km/h}$ is brought to a halt within $4\text{ s}$ after applying the brakes. The distance travelled by the bus during this time (Assume the retardation is uniform) is ________ $\text{m}$.

Two parallel long current carrying wires separated by a distance $2r$ are shown in the figure. The ratio of magnetic field at $A$ to the magnetic field produced at $C$ is $\frac{x}{7}$. The value of $x$ is __________.

The disintegration energy $Q$ for the nuclear fission of ${}^{235}\text{U} \rightarrow {}^{140}\text{Ce} + {}^{94}\text{Zr} + n$ is _______ $\text{MeV}$. Given atomic masses of ${}^{235}\text{U} : 235.0439u;\ {}^{140}\text{Ce} : 139.9054u,\ {}^{94}\text{Zr} : 93.9063u;\ n : 1.0086u$, Value of $c^{2} = 931\text{ MeV/u}$.

In simple harmonic motion, the total mechanical energy of given system is $E$. If mass of oscillating particle $P$ is doubled then the new energy of the system for same amplitude is:

The displacement of a particle executing SHM is given by $x = 10\sin\left(\omega t + \frac{\pi}{3}\right)\text{ m}$. The time period of motion is $3.14\text{ s}$. The velocity of the particle at $t = 0$ is _______ $\text{m/s}$.

A light ray is incident on a glass slab of thickness $4\sqrt{3}\text{ cm}$ and refractive index $\sqrt{2}$ The angle of incidence is equal to the critical angle for the glass slab with air. The lateral displacement of ray after passing through glass slab is ______ $\text{cm}$.

(Given $\sin 15^\circ = 0.25$)

Identify the logic gate given in the circuit:

Which of the diode circuits shows correct biasing used for the measurement of dynamic resistance of p-n junction diode:

Given below are two statements:

Statement I: The contact angle between a solid and a liquid is a property of the material of the solid and liquid as well.

Statement II: The rise of a liquid in a capillary tube does not depend on the inner radius of the tube. In the light of the above statements, choose the correct answer from the options given below:

The translational degrees of freedom $(f_t)$ and rotational degrees of freedom $(f_r)$ of $\text{CH}_4$ molecule are:

A sample of gas at temperature $T$ is adiabatically expanded to double its volume. Adiabatic constant for the gas is $\gamma = 3/2$. The work done by the gas in the process is:

$(\mu = 1$ mole $)$

Applying the principle of homogeneity of dimensions, determine which one is correct, where $T$ is time period, $G$ is gravitational constant, $M$ is mass, $r$ is radius of orbit.

The width of one of the two slits in a Young's double slit experiment is 4 times that of the other slit. The ratio of the maximum to the minimum intensity in the interference pattern is:

A body of $m\text{ kg}$ slides from rest along the curve of vertical circle from point $A$ to $B$ in frictionless path. The velocity of the body at $B$ is:

(given, $R = 14\text{ m}, g = 10\text{ m/s}^2$ and $\sqrt{2} = 1.4$)