JEE Main 2025 Apr 7 Shift 2 — Physics

The dimension of $\sqrt{\dfrac{\mu_0}{\epsilon_0}}$ is equal to that of :

($\mu_0$ = Vacuum permeability and $\epsilon_0$ = Vacuum permittivity)

Match List - I with List - II.

List - I	List - II
(A) Mass density	(I) $[\mathrm{ML^2T^{-3}}]$
(B) Impulse	(II) $[\mathrm{MLT^{-1}}]$
(C) Power	(III) $[\mathrm{ML^2T^{0}}]$
(D) Moment of inertia	(IV) $[\mathrm{ML^{-3}T^{0}}]$

Choose the correct answer from the options given below :

An object with mass 500 g moves along $x$-axis with speed $v = 4\sqrt{x}$ m/s. The force acting on the object is :

A helicopter flying horizontally with a speed of 360 km/h at an altitude of 2 km, drops an object at an instant. The object hits the ground at a point O, 20 s after it is dropped. Displacement of 'O' from the position of helicopter where the object was released is :

(use acceleration due to gravity $g = 10\ \mathrm{m/s^2}$ and neglect air resistance)

Which one of the following forces cannot be expressed in terms of potential energy ?

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

Assertion (A) : The radius vector from the Sun to a planet sweeps out equal areas in equal intervals of time and thus areal velocity of planet is constant.

Reason (R) : For a central force field the angular momentum is a constant.

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

A capillary tube of radius 0.1 mm is partly dipped in water (surface tension 70 dyn/cm and glass water contact angle $\approx 0°$) with 30° inclined with the vertical. The length of water risen in the capillary is __________ cm. (Take $g = 9.8\ \mathrm{m/s^2}$)

The helium and argon are put in the flask at the same room temperature (300 K). The ratio of average kinetic energies (per molecule) of helium and argon is :

(Give : Molar mass of helium $= 4$ g/mol, Molar mass of argon $= 40$ g/mol)

Match List - I with List - II.

List - I	List - II
(A) Isothermal	(I) $\Delta W$ (work done) $= 0$
(B) Adiabatic	(II) $\Delta Q$ (supplied heat) $= 0$
(C) Isobaric	(III) $\Delta U$ (change in internal energy) $\neq 0$
(D) Isochoric	(IV) $\Delta U = 0$

Choose the correct answer from the options given below :

The equation of a wave travelling on a string is $y = \sin[20\pi x + 10\pi t]$, where $x$ and $t$ are distance and time in SI units. The minimum distance between two points having the same oscillating speed is :

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

Assertion (A) : Magnetic monopoles do not exist.

Reason (R) : Magnetic field lines are continuous and form closed loops.

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

A dipole with two electric charges of 2 $\mu$C magnitude each, with separation distance 0.5 $\mu$m, is placed between the plates of a capacitor such that its axis is parallel to an electric field established between the plates when a potential difference of 5 V is applied. Separation between the plates is 0.5 mm. If the dipole is rotated by 30° from the axis, it tends to realign in the direction due to a torque. The value of torque is :

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

Assertion (A) : The outer body of an air craft is made of metal which protects persons sitting inside from lightning-strikes.

Reason (R) : The electric field inside the cavity enclosed by a conductor is zero.

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

The unit of $\sqrt{\dfrac{2I}{\epsilon_0 c}}$ is :

(I = intensity of an electromagnetic wave, c : speed of light)

A mirror is used to produce an image with magnification of $\dfrac{1}{4}$. If the distance between object and its image is 40 cm, then the focal length of the mirror is __________.

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

Assertion (A) : Refractive index of glass is higher than that of air.

Reason (R) : Optical density of a medium is directly proportionate to its mass density which results in a proportionate refractive index.

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

A transparent block A having refractive index $\mu = 1.25$ is surrounded by another medium of refractive index $\mu = 1.0$ as shown in figure. A light ray is incident on the flat face of the block with incident angle $\theta$ as shown in figure. What is the maximum value of $\theta$ for which light suffers total internal reflection at the top surface of the block ?

a ray enters the vertical left face of rectangular block A ($\mu_2 = 1.25$, surrounded by $\mu_1 = 1.0$) at angle $\theta$ to the horizontal normal, refracts, and strikes the top surface at the critical angle $\theta_C$

A photoemissive substance is illuminated with a radiation of wavelength $\lambda_i$ so that it releases electrons with de-Broglie wavelength $\lambda_e$. The longest wavelength of radiation that can emit photoelectron is $\lambda_o$. Expression for de-Broglie wavelength is given by :

(m : mass of the electron, h : Planck's constant and c : speed of light)

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

Assertion (A) : The density of the copper $\left(^{64}_{29}\mathrm{Cu}\right)$ nucleus is greater than that of the carbon $\left(^{12}_{6}\mathrm{C}\right)$ nucleus.

Reason (R) : The nucleus of mass number A has a radius proportional to $A^{1/3}$.

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

Consider the following logic circuit.

logic circuit — inputs A and B feed an AND gate; a branch of the inputs, one passed through a NOT gate, feeds an OR gate; the AND and OR outputs feed a NAND gate whose output is Y

The output is $Y = 0$ when :

M and R be the mass and radius of a disc. A small disc of radius $R/3$ is removed from the bigger disc as shown in figure. The moment of inertia of remaining part of bigger disc about an axis AB passing through the centre O and perpendicular to the plane of disc is $\dfrac{4}{x}\,MR^2$. The value of $x$ is __________.

a disc of radius R centred at O with vertical axis AB; a small disc of radius R/3 centred at O' is removed near the left edge, with O' on the horizontal diameter

Two cylindrical rods A and B made of different materials, are joined in a straight line. The ratios of lengths, radii and thermal conductivites of these rods are : $\dfrac{L_A}{L_B} = \dfrac{1}{2}$, $\dfrac{r_A}{r_B} = 2$ and $\dfrac{K_A}{K_B} = \dfrac{1}{2}$. The free ends of rods A and B are maintained at 400 K, 200 K, respectively. The temperature of rods interface is __________ K, when equilibrium is established.

An inductor of reactance 100 $\Omega$, a capacitor of reactance 50 $\Omega$, and a resistor of resistance 50 $\Omega$ are connected in series with an AC source of 10 V, 50 Hz. Average power dissipated by the circuit is __________ W.

A parallel plate capacitor has charge $5 \times 10^{-6}$ C. A dielectric slab is inserted between the plates and almost fills the space between the plates. If the induced charge on one face of the slab is $4 \times 10^{-6}$ C then the dielectric constant of the slab is __________.

The electric field in a region is given by $\vec{E} = \left(2\hat{i} + 4\hat{j} + 6\hat{k}\right) \times 10^3$ N/C. The flux of the field through a rectangular surface parallel to $x$-$z$ plane is $6.0\ \mathrm{Nm^2C^{-1}}$. The area of the surface is __________ $\mathrm{cm^2}$.