JEE Main 2026 Physics Paper: 23 Jan, Shift 2

A parallel plate capacitor with plate separation 5 mm is charged by a battery. On introducing a mica sheet of 2 mm and maintaining the connections of the plates with the terminals of the battery, it is found that it draws $25\%$ more charge from the battery. The dielectric constant of mica is ______

To compare EMF of two cells using potentiometer the balancing lengths obtained are 200 cm and 150 cm. The least count of scale is 1 cm. The percentage error in the ratio of EMFs is ______

A circular loop of radius 7 cm is placed in uniform magnetic field of 0.2 T directed perpendicular to plane of loop. The loop is converted into a square loop in 0.5 s. The EMF induced in the loop is ______ mV.

Suppose a long solenoid of 100 cm length, radius 2 cm having 500 turns per unit length, carries a current $I = 10 \sin(\omega t)\text{ A}$, where $\omega = 1000\text{ rad/s}$. A circular conducting loop $(B)$ of radius 1 cm coaxially slided through the solenoid at a speed $v = 1\text{ cm/s}$. The r.m.s. current through the loop when the coil $B$ is inserted 10 cm inside the solenoid is $\frac{\alpha}{\sqrt{2}} \mu A$. The value of $\alpha$ is ______. [Resistance of the loop $= 10\,\Omega$ ]

The ratio of speeds of electromagnetic waves in vacuum and a medium, having dielectric constant $k = 3$ and permeability of $\mu = 2\mu_0$, is ( $\mu_0 =$ permeability of vacuum)

Two short dipoles $(A, B), A$ having charges $\pm 2\,\mu\text{C}$ and length 1 cm and $B$ having charges $\pm 4\,\mu\text{C}$ and length 1 cm are placed with their centres 80 cm apart as shown in the figure. The electric field at a point $P$, equi-distant from the centres of both dipoles is ______ N/C.

Two charges $7\mu\text{C}$ and $-2\mu\text{C}$ are placed at $(-9, 0, 0)\text{ cm}$ and $(9, 0, 0)\text{ cm}$ respectively in an external field $E = \frac{A}{r^2}\hat{r}$, where $A = 9 \times 10^{5}\text{ N/C}\cdot\text{m}^2$. Considering the potential at infinity is 0, the electrostatic energy of the configuration is ______ J.

A block is sliding down on an inclined plane of slope $\theta$ and at an instant $t = 0$ this block is given an upward momentum so that it starts moving up on the inclined surface with velocity $u$. The distance $(S)$ travelled by the block before its velocity become zero, is ______.

(g = gravitational acceleration)

A paratrooper jumps from an aeroplane and opens a parachute after 2 s of free fall and starts decelerating with $3\text{ m/s}^2$. At 10 m height from ground, while descending with the help of parachute, the speed of paratrooper is $5\text{ m/s}$. The initial height of the airplane is ______ m.

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

The current passing through a conducting loop in the form of equilateral triangle of side $4\sqrt{3}\text{ cm}$ is 2 A. The magnetic field at its centroid is $\alpha \times 10^{-5}\text{ T}$. The value of $\alpha$ is ______.

(Given: $\mu_0 = 4\pi \times 10^{-7}$ SI units)

The average energy released per fission for the nucleus of ${}^{235}_{92}\text{U}$ is 190 MeV. When all the atoms of 47 g pure ${}^{235}_{92}\text{U}$ undergo fission process, the energy released is $\alpha \times 10^{23}\text{ MeV}$. The value of $\alpha$ is ______. (Avogadro Number $= 6 \times 10^{23}$ per mole)

Which of the following pair of nuclei are isobars of the element?

The size of the images of an object, formed by a thin lens are equal when the object is placed at two different positions 8 cm and 24 cm from the lens. The focal length of the lens is ______ cm.

Suppose there is a uniform circular disc of mass $M\text{ kg}$ and radius $r\text{ m}$ shown in figure. The shaded regions are cut out from the disc. The moment of inertia of the remainder about the axis $A$ of the disc is given by $\frac{x}{256}Mr^2$. The value of $x$ is ______.

For the given logic gate circuit, which of the following is the correct truth table?

An air bubble of volume $2.9\text{ cm}^{3}$ rises from the bottom of a swimming pool of 5 m deep. At the bottom of the pool water temperature is $17^\circ\text{C}$. The volume of the bubble when it reaches the surface, where the water temperature is $27^\circ\text{C}$, is $\underline{\qquad}\ \text{cm}^{3}$.

( $g = 10\text{ m/s}^{2}$, density of water $= 10^{3}\text{ kg/m}^{3}$, and 1 atm pressure is $10^{5}\text{ Pa}$)

One mole of an ideal diatomic gas expands from volume $V$ to $2V$ isothermally at a temperature $27^\circ\text{C}$ and does $W$ joule of work. If the gas undergoes same magnitude of expansion adiabatically from $27^\circ\text{C}$ doing the same amount of work $W$, then its final temperature will be (close to) $\underline{\hspace{3em}}\ ^\circ\text{C}.\ (\log_e 2 = 0.693)$

The internal energy of a monoatomic gas is 3nRT. One mole of helium is kept in a cylinder having internal cross section area of $17\text{ cm}^{2}$ and fitted with a light movable frictionless piston. The gas is heated slowly by suppling 126 J heat. If the temperature rises by $4^\circ\text{C}$, then the piston will move ______ cm.

(atmospheric pressure $= 10^{5}\text{ Pa}$)

A ball of radius $r$ and density $\rho$ dropped through a viscous liquid of density $\sigma$ and viscosity $\eta$ attains its terminal velocity at time $t$, given by $t = A\rho^{a}r^{b}\eta^{c}\sigma^{d}$, where $A$ is a constant and $a, b, c$ and $d$ are integers. The value of $\frac{b+c}{a+d}$ is ______.

A small metallic sphere of diameter 2 mm and density $10.5\text{ g/cm}^{3}$ is dropped in glycerine having viscosity 10 Poise and density $1.5\text{ g/cm}^{3}$ respectively. The terminal velocity attained by the sphere is $\underline{\hspace{3em}}\text{ cm/s}$.

$\left(\pi = \frac{22}{7}\right.$ and $g = 10\text{ m/s}^{2})$

The velocity of sound in air is doubled when the temperature is raised from $0^\circ\text{C}$ to $\alpha^\circ\text{C}$. The value of $\alpha$ is ______.

When an unpolarized light falls at a particular angle on a glass plate (placed in air), it is observed that the reflected beam is linearly polarized. The angle of refracted beam with respect to the normal is ______.

$(\tan^{-1}(1.52) = 57.7^\circ$, refractive indices of air and glass are 1.00 and 1.52, respectively.)

A bead $P$ sliding on a frictionless semi-circular string $(ACB)$ and it is at point $S$ at $t = 0$ and at this instant the horizontal component of its velocity is $v$. Another bead $Q$ of the same mass as $P$ is ejected from point $A$ at $t = 0$ along the horizontal string $AB$, with the speed $v$, friction between the beads and the respective strings may be neglected in both cases. Let $t_P$ and $t_Q$ be the respective times taken by beads $P$ and $Q$ to reach the point $B$, then the relation between $t_P$ and $t_Q$ is