JEE Main 2025 Jan 24 Shift 2 — Physics

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

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

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 :

The position vector of a moving body at any instant of time is given as $\vec{r} = \left(5t^2\,\hat{i} - 5t\,\hat{j}\right)\,\mathrm{m}$. The magnitude and direction of velocity at $t = 2\,\mathrm{s}$ 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 temperature of a body in air falls from $40°\mathrm{C}$ to $24°\mathrm{C}$ in 4 minutes. The temperature of the air is $16°\mathrm{C}$. The temperature of the body in the next 4 minutes will be :

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

P–V diagram with P (in kPa) on the vertical axis and V (in cc) on the horizontal axis; a circle spans 200–400 on both axes with A at the right (400 cc), B at the top (400 kPa), C at the left (200 cc) and D at the bottom (200 kPa); the cycle follows the upper semicircle through B and the horizontal line C→A through the centre, the lower semicircle through D being dotted

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 adiabatic process.

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 $x_0 = 1$ m. The kinetic energy (K) of the particle as a function of $x$ is correctly represented by the graph

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

Assertion (A) : A 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 long straight wire of circular cross-section of radius 'a' carries a steady current I. The current I is uniformly distributed across this cross-section. The variation of magnitude of magnetic field B with distance r from the centre of the wire is represented by the graph :

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

two squares of side 'a'. Configuration (1): identical charges $+q_0$ at the four corners A, B, C, D; G, E, H, F are the midpoints of sides AB, BC, DC and AD respectively, with centre O. Configuration (2): the same charges $+q_0$ placed at the midpoints G, E, H and F

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 :

N charges, each of value q, are placed at equal intervals on a circle of radius R. The circle rotates about its axis with an angular velocity $\omega$ as shown in the figure. A relatively large Amperian loop B encircles the whole circle whereas a relatively small Amperian loop A encircles a small segment. The difference between the enclosed currents, $I_A - I_B$, for the given Amperian loops is

a circle of radius R carrying N equally spaced charges, rotating with angular velocity ω about its axis; a large Amperian loop B threads the entire circle while a small Amperian loop A encircles a small segment of it

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

Young's double slit inteference 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 :

In a Young's double slit experiment, three polarizers are kept as shown in the figure. The transmission axes of $\mathrm{P}_1$ and $\mathrm{P}_2$ are orthogonal to each other. The polarizer $\mathrm{P}_3$, whose transmission axis is at $45°$ to the transmission axes of $\mathrm{P}_1$ and $\mathrm{P}_2$, covers both the slits. An unpolarized light of wavelength $\lambda$ and intensity $\mathrm{I}_0$ is incident on $\mathrm{P}_1$ and $\mathrm{P}_2$. At a point after $\mathrm{P}_3$, where the path difference between the light waves from $s_1$ and $s_2$ is $\frac{\lambda}{3}$, the intensity is :

unpolarized light of wavelength λ and intensity I₀ is incident on polarizers P₁ and P₂ placed over slits s₁ and s₂ respectively; polarizer P₃ placed after them covers both slits

In photoelectric effect, the stopping potential $(\mathrm{V}_0)$ v/s frequency $(\nu)$ curve is plotted.

(h is the Planck's constant and $\phi_0$ is work function of metal)

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

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

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

(D) The value of electric charge of electron is not required to determine h using the $\mathrm{V}_0$ v/s $\nu$ curve.

(E) The work function can be estimated without knowing the value of h.

Choose the correct answer from the options given below :

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

logic circuit — inputs X and Y feed an OR gate; the OR gate's output passes through a NOT (inverting) gate to give the final output

(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 :

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

a string of length L fixed to the ceiling makes angle θ with the vertical; tension T acts along the string and the mass at its end moves in a horizontal circle of radius R

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

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

The ratio of the power of a light source $\mathrm{S}_1$ to that of the light source $\mathrm{S}_2$ is 2. $\mathrm{S}_1$ is emitting $2 \times 10^{15}$ photons per second at 600 nm. If the wavelength of the source $\mathrm{S}_2$ is 300 nm, then the number of photons per second emitted by $\mathrm{S}_2$ is ______ $\times 10^{14}$.