JEE Main 2025 Physics Paper: 24 Jan, Shift 2

The energy E and momentum p of a moving body of mass m are related by some equation. Given that c represents the speed of light, identify the correct equation

A string of length $L$ is fixed at one end and carries a mass of $M$ at the other end. The mass makes $\left(\frac{3}{\pi}\right)$ rotations per second about the vertical axis passing through end of the string as shown. The tension in the string is __________ ML.

In photoelectric effect, the stopping potential $(\mathrm{V}_0)\text{ v/s}$ frequency $(v)$ curve is plotted. ( h is the Planck's constant and $\phi_0$ is work function of metal)

(A) $\mathrm{V}_0\text{ v/s } v$ is linear.

(B) The slope of $\mathrm{V}_0\text{ v/s } v$ curve $= \frac{\phi_0}{\mathrm{h}}$

(C) h constant is related to the slope of $\mathrm{V}_0\text{ v/s } v$ line.

(D) The value of electric charge of electron is not required to determine h using the $\mathrm{V}_0\text{ v/s } v$ curve. (E) The work function can be estimated without knowing the value of $h$.

Choose the correct answer from the options given below:

The ratio of the power of a light source $S_1$ to that of the light source $S_2$ is $2.\ S_1$ is emitting $2 \times 10^{15}$ photons per second at 600 nm. If the wavelength of the source $S_2$ is 300 nm, then the number of photons per second emitted by $S_2$ is __________ $\times 10^{14}$.

Arrange the following in the ascending order of wavelength $(\lambda)$:

(A) Microwaves $(\lambda_1)$

(B) Ultraviolet rays $(\lambda_2)$

(C) Infrared rays $(\lambda_3)$

(D) X-rays $(\lambda_4)$

Choose the most appropriate answer from the options given below:

A small uncharged conducting sphere is placed in contact with an identical sphere but having $4 \times 10^{-8}\text{ C}$ charge and then removed to a distance such that the force of repulsion between them is $9 \times 10^{-3}\text{ N}$. The distance between them is (Take $\frac{1}{4\pi\epsilon_0}$ as $9 \times 10^{9}$ in SI units)

In the first configuration (1) as shown in the figure, four identical charges $(q_0)$ are kept at the corners A, B, C and D of square of side length ' $a$ '. In the second configuration (2), the same charges are shifted to mid points $G, E, H$ and $F$, of the square. If $K = \frac{1}{4\pi\epsilon_0}$, the difference between the potential energies of configuration (2) and (1) is given by:

The increase in pressure required to decrease the volume of a water sample by $0.2\%$ is $P \times 10^{5}\text{ N m}^{-2}$. Bulk modulus of water is $2.15 \times 10^{9}\text{ N m}^{-2}$. The value of P is _________.

Acceleration due to gravity on the surface of earth is ' $g$ '. If the diameter of earth is reduced to one third of its original value and mass remains unchanged, then the acceleration due to gravity on the surface of the earth is ________ g.

The temperature of a body in air falls from $40^\circ\text{C}$ to $24^\circ\text{C}$ in 4 minutes. The temperature of the air is $16^\circ\text{C}$. The temperature of the body in the next 4 minutes will be:

The increase in pressure required to decrease the volume of a water sample by $0.2\%$ is $\text{P} \times 10^{5}\text{ Nm}^{-2}$. Bulk modulus of water is $2.15 \times 10^{9}\text{ Nm}^{-2}$. The value of P is _________.

A long straight wire of a circular cross-section with radius ' a ' carries a steady current I. The current I is uniformly distributed across this cross-section. The plot of magnitude of magnetic field B with distance $r$ from the centre of the wire is given by

N equally spaced charges each of value q, are placed on a circle of radius R. The circle rotates about its axis with an angular velocity $\omega$ as shown in the figure. A bigger Amperian loop B encloses the whole circle where as a smaller Amperian loop A encloses a small segment. The difference between enclosed currents, $I_A - I_B$, for the given Amperian loops is

A tightly wound long solenoid carries a current of 1.5 A. An electron is executing uniform circular motion inside the solenoid with a time period of 75 ns. The number of turns per metre in the solenoid is _________.

[Take mass of electron$\mathrm{m_e} = 9 \times 10^{-31}\text{ kg} \quad \frac{\mathrm{N}}{\mathrm{A}^2}, 1\text{ ns} = 10^{-9}\text{ s}]$, charge of electron $|\mathrm{q_e}| = 1.6 \times 10^{-19}\text{ C}, \mu_0 = 4\pi \times 10^{-7}$

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A): An electron in a certain region of uniform magnetic field is moving with constant velocity in a straight line path.

Reason (R): The magnetic field in that region is along the direction of velocity of the electron. In the light of the above statements, choose the correct answer from the options given below:

A particle oscillates along the $x$-axis according to the law, $x(t) = x_0\sin^2\left(\frac{t}{2}\right)$ where $x_0 = 1\text{ m}$. The kinetic energy $(K)$ of the particle as a function of $x$ is correctly represented by the graph

The position vector of a moving body at any instant of time is given as$\vec{r} = \left(5t^{2}\hat{i} - 5t\hat{j}\right)\text{ m}$. The magnitude and direction of velocity at $t = 2\text{ s}$ is,

A photograph of a landscape is captured by a drone camera at a height of 18 km. The size of the camera film is $2\text{ cm} \times 2\text{ cm}$ and the area of the landscape photographed is $400\text{ km}^{2}$. The focal length of the lens in the drone camera is:

A solid sphere is rolling without slipping on a horizontal plane. The ratio of the linear kinetic energy of the centre of mass of the sphere and rotational kinetic energy is:

A solid sphere and a hollow sphere of the same mass and of same radius are rolled on an inclined plane. Let the time taken to reach the bottom by the solid sphere and the hollow sphere be $t_1$ and $t_2$, respectively, then

The output of the circuit is low (zero) for:

(A) $X = 0, Y = 0$

(B) $X = 0, Y = 1$

(C) $X = 1, Y = 0$

(D) $X = 1, Y = 1$

Choose the correct answer from the options given below:

The magnitude of heat exchanged by a system for the given cyclic process ABCA (as shown in figure) is (in SI unit):

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A): In an insulated container, a gas is adiabatically shrunk to half of its initial volume. The temperature of the gas decreases.

Reason (R): Free expansion of an ideal gas is an irreversible and an adiabatic process. In the light of the above statements, choose the correct answer from the options given below:

Which of the following figure represents the relation between Celsius and Fahrenheit temperatures?

In a Young's double slit experiment, three polarizers are kept as shown in the figure. The transmission axes of $P_1$ and $P_2$ are orthogonal to each other. The polarizer $P_3$ covers both the slits with its transmission axis at $45^\circ$ to those of $P_1$ and $P_2$. An unpolarized light of wavelength $\lambda$ and intensity $I_0$ is incident on $P_1$ and $P_2$. The intensity at a point after $P_3$ where the path difference between the light waves from $s_1$ and $s_2$ is $\frac{\lambda}{3}$, is

Young's double slit interference apparatus is immersed in a liquid of refractive index 1.44. It has slit separation of 1.5 mm. The slits are illuminated by a parallel beam of light whose wavelength in air is 690 nm. The fringe-width on a screen placed behind the plane of slits at a distance of 0.72 m, will be: