JEE Main 2026 Physics Paper: 8 Apr, Shift 2

The stored charge in the capacitor in steady state of the following circuit is $\rule{2.5em}{0.4pt}\ \mu\text{C}$.

A parallel plate capacitor is having separation between plates 0.885 mm. It has a capacitance of $1\ \mu\text{F}$ when the space between the plates is filled with an insulating material of resistivity $1\times 10^{13}\ \Omega\text{ m}$ and resistance $17.7\times 10^{14}\ \Omega$. Relative permittivity of the insulating material is $\alpha\times 10^{7}$. The value of $\alpha$ is ______.

(Take permittivity of free space $=8.85\times 10^{-12}\text{ F/m}$)

A car moving with a speed of $54\text{ km/h}$ takes a turn of radius 20 m. A simple pendulum is suspended from the ceiling of the car. Determine the angle made by the string of the pendulum with the vertical during the turning. (Take $g = 10\text{ m/s}^2$)

$K_1$ and $K_2$ be the maximum kinetic energies of photoelectrons emitted from a surface of a given material for the light of wavelength $\lambda_1$ and $\lambda_2$, respectively. If $\lambda_1 = 2\lambda_2$ then the work function of material is given by:

A monochromatic source of light operating at 15 kW emits $2.5 \times 10^{22}$ photons $/\text{s}$. The region of an electromagnetic spectrum to which the emitted electromagnetic radiation belongs to ______. (Take $h = 6.6 \times 10^{-34}\text{ J.s}$ and $c = 3 \times 10^{8}\text{ m/s}$ ).

A 30 cm long solenoid has 10 turns per cm and area of $5\text{ cm}^{2}$. The current through the solenoid coil varies from 2 A to 4 A in 3.14 s. The e.m.f. induced in the coil is $\alpha \times 10^{-5}\text{ V}$. The value $\alpha$ is ______.

Two point charges $q_1 = 3\ \mu\text{C}$ and $q_2 = -4\ \mu\text{C}$ are placed at points $(2\hat{i} + 3\hat{j} + 3\hat{k})$ and $(\hat{i} + \hat{j} + \hat{k})$ respectively. Force on charge $q_2$ is ______ N. (Take $\frac{1}{4\pi\epsilon_0} = 9 \times 10^{9}$ SI Units)

A liquid of density $600\text{ kg/m}^3$ flowing steadily in a tube of varying cross-section. The cross-section at a point $A$ is $1.0\text{ cm}^2$ and that at $B$ is $20\text{ mm}^2$. Both the points $A$ and $B$ are in same horizontal plane, the speed of the liquid at $A$ is $10\text{ cm/s}$. The difference in pressures at $A$ and $B$ points is ______ Pa.

A gas balloon is going up with a constant velocity of $10\text{ m/s}$. When this balloon reached a height of 75 m, a stone is dropped from it and balloon keeps moving up with the same velocity. The height of the balloon when the stone hits the ground is ______ m. (Take $g = 10\text{ m/s}^2$)

A current carrying circular loop of radius 2 cm with unit normal $\hat{n} = \frac{\hat{k} + \hat{i}}{\sqrt{2}}$ is placed in a magnetic field, $\vec{B} = B_o(3\hat{i} + 2\hat{k})$. If $B_o = 4 \times 10^{-3}\text{ T}$ and current $I = 100\sqrt{2}\text{ A}$, the torque experienced by the loop is ______ Wb.A. ( $\pi = 3.14$)

A 5 mg particle carrying a charge of $5\pi \times 10^{-6}\text{ C}$ is moving with velocity of $(3\hat{i} + 2\hat{k}) \times 10^{-2}\text{ m/s}$ in a region having magnetic field $\vec{B} = 0.1\hat{k}\text{ Wb/m}^2$. It moves a distance of $\alpha$ meter along $\hat{k}$ when it completes 5 revolutions. The value of $\alpha$ is ______。

Two radioactive substances A and B of mass numbers 200 and 212 respectively, shows spontaneous $\alpha$-decay with same $Q$ value of 1 MeV. The ratio of energies of $\alpha$-rays produced by A and B is ______.

The frequency of oscillation of a mass $m$ suspended by a spring is $v_1$. If the length of the spring is cut to half, the same mass oscillates with frequency $v_2$. The value of $v_2/v_1$ is ______.

Two identical bodies, projected with the same speed at two different angles cover the same horizontal range $R$. If the time of flight of these bodies are 5 s and 10 s, respectively, then the value of $R$ is

______ m. (Take $g = 10\text{ m/s}^{2}$)

A thin biconvex lens is prepared from the glass $(\mu = 1.5)$ both curved surfaces of which have equal radii of 20 cm each. Left side surface of the lens is silvered from outside to make it reflecting. To have the position of image and object at the same place, the object should be placed, from the lens at a distance of ______ cm.

Light ray incident along a vector $\overrightarrow{AO}\left(\overrightarrow{AO} = 2\hat{i} - 3\hat{j}\right)$ emerges out along vector $\overrightarrow{OB}\left(\overrightarrow{OB} = C\hat{i} - 4\hat{j}\right)$ as shown in the figure below. The value of $C$ is ______.

A solid cylinder having radius $R$ and length $L$ is slipping on a rough horizontal plane. At time $t = 0$ the cylinder has a translational velocity $v_0 = 49\text{ m/s}$, perpendicular to its axis and a rotational velocity $v_0/4R$ about the centre. The time taken by the cylinder to start rolling is ______ seconds. (coefficient of kinetic friction $\mu_K = 0.25$ and $g = 9.8\text{ m/s}^{2}$)

The output $Y$ for the given inputs $A$ and $B$ to the circuit is:

Initial pressure and volume of a monoatomic ideal gas are $P$ and $V$. The change in internal energy of this gas in adiabatic expansion to volume $V$final $= 27\,V$ is ______ J.

One mole of diatomic gas having rotational modes only is kept in a cylinder with a piston system. The cross-section area of the cylinder is $4\text{ cm}^{2}$. The gas is heated slowly to raise the temperature by $1.2^\circ\text{C}$ during which the piston moves by 25 mm. The amount of heat supplied to the gas is ______ J. (Atmospheric pressure $= 100\text{ kPa}, R = 8.3\text{ J/mol.K}$) (Neglect mass of the piston)

Consider the equation $H = \frac{x^p \epsilon^q E^r}{t^s}$

Where $H =$ magnetic field intensity; $E =$ electric field, $\epsilon =$ permittivity, $x =$ distance, $t =$ time The values of $p, q, r$ and $s$ respectively are:

A new unit ( $\alpha$) of length is chosen such that it is equal to the speed of light in vacuum. What is the distance between Venus and Earth in terms of $\alpha$ units if light takes 6 min. 40 s to cover this distance?

A spherical liquid drop of radius $R$ acquires the terminal velocity $v_1$ when falls through a gas of viscosity $\eta$. Now the drop is broken into 64 identical droplets and each droplet acquires terminal velocity $v_2$ falling through the same gas. The ratio of terminal velocities $v_1/v_2$ is ______.

Some distant star is to be observed by some telescope of diameter of objective lens $a$, at an angular resolution of $3.0 \times 10^{-7}$ radian. If the wavelength of light from the star reaching the telescope is 500 nm, the minimum diameter of the objective lens of the telescope is ______ cm. (nearest interger)