JEE Main 2026 Physics Paper: 22 Jan, Shift 1

$7.9\text{ MeV }\alpha$-particle scatters from a target material of atomic number 79. From the given data the estimated diameter of nuclei of the target material is (approximately) ______ m.

$\Bigg[\frac{1}{4\pi\epsilon_0} = 9 \times 10^{9}\text{ Nm}^2/\text{C}^2$ and electron charge $= 1.6 \times 10^{-19}\text{ C}\Bigg]$

A meter bridge with two resistances $R_1$ and $R_2$ as shown in figure was balanced (null point) at 40 cm from the point $P$. The null point changed to 50 cm from the point $P$, when $16\ \Omega$ resistance is connected in parallel to $R_2$. The values of resistances $R_1$ and $R_2$ are ______.

Three identical coils $C_1, C_2$ and $C_3$ are closely placed such that they share a common axis. $C_2$ is exactly midway. $C_1$ carries current $I$ in anti-clockwise direction while $C_3$ carries current $I$ in clockwise direction. An induced current flows through $C_2$ will be in clockwise direction when

$XPQY$ is a vertical smooth long loop having a total resistance $R$ where $PX$ is parallel to $QY$ and separation between them is $l$. A constant magnetic field $B$ perpendicular to the plane of the loop exists in the entire space. A rod $CD$ of length $L(L > l)$ and mass $m$ is made to slide down from rest under the gravity as shown in figure. The terminal speed acquired by the rod is $\underline{\qquad}\ \text{m/s. }(g =$ acceleration due to gravity)

Inductance of a coil with $10^{4}$ turns is 10 mH and it is connected to a dc source of 10 V with internal resistance of $10\ \Omega$. The energy density in the inductor when the current reaches $\left(\frac{1}{e}\right)$ of its maximum value is $\alpha \pi \times \frac{1}{e^2}\text{ J/m}^{3}$. The value of $\alpha$ is

______.

$\left(\mu_0 = 4\pi \times 10^{-7}\text{ Tm/A}\right).$

The electric field of a plane electromagnetic wave, travelling in an unknown nonmagnetic medium is given by,

$E_y = 20 \sin\left(3 \times 10^{6} x - 4.5 \times 10^{14} t\right)\text{ V/m}$

(where $x, t$ and other values have S.I. units). The dielectric constant of the medium is ______ (speed of light in free space is $3 \times 10^{8}\text{ m/s}$)

Six point charges are kept $60^\circ$ apart from each other on the circumference of a circle of radius $R$ as shown in figure. The net electric field at the center of the circle is ______.

( $\epsilon_0$ is permittivity of free space)

Electric field in a region is given by $\vec{E} = Ax\hat{i} + By\hat{j}$, where $A = 10\text{ V/m}^2$ and $B = 5\text{ V/m}^2$. If the electric potential at a point $(10, 20)$ is 500 V, then the electric potential at origin is ______ V.

A simple pendulum has a bob with mass $m$ and charge $q$. The pendulum string has negligible mass. When a uniform and horizontal electric field $\vec{E}$ is applied, the tension in the string changes. The final tension in the string, when pendulum attains an equilibrium position is ______.

Given below are two statements:

Statement I: Pressure of a fluid is exerted only on a solid surface in contact as the fluid-pressure does not exist everywhere in a still fluid.

Statement II: Excess potential energy of the molecules on the surface of a liquid, when compared to interior, results in surface tension.

In the light of the above statements, choose the correct answer from the options given below

The escape velocity from a spherical planet $A$ is $10\text{ km/s}$. The escape velocity from another planet $B$ whose density and radius are $10\%$ of those of planet $A$, is $\underline{\hspace{3em}}\text{ m/s}$.

Net gravitational force at the center of a square is found to be $F_1$ when four particles having mass $M, 2M, 3M$ and $4M$ are placed at the four corners of the square as shown in figure and it is $F_2$ when the positions of $3M$ and $4M$ are interchanged. The ratio $\frac{F_1}{F_2}$ is $\frac{\alpha}{\sqrt{5}}$. The value of $\alpha$ is ______.

Rods $x$ and $y$ of equal dimensions but of different materials are joined as shown in figure. Temperatures of end points $A$ and $F$ are maintained at $100^\circ\text{C}$ and $40^\circ\text{C}$ respectively. Given the thermal conductivity of $\text{rod } x$ is three times of that of $\text{rod } y$, the temperature at junction points $B$ and $E$ are (close to):

The minimum frequency of photon required to break a particle of mass 15.348 amu into $4\alpha$ particles is ______ kHz.

[mass of He nucleus = $4.002\text{ amu}, 1\text{ amu} = 1.66 \times 10^{-27}\text{ kg}, \text{h} = 6.6 \times 10^{-34}\text{ J.s}$ and $\text{c} = 3 \times 10^{8}\text{ m/s}$ ]

A projectile is thrown upward at an angle $60^\circ$ with the horizontal. The speed of the projectile is $20\text{ m/s}$ when its direction of motion is $45^\circ$ with the horizontal. The initial speed of the projectile is $\underline{\qquad}\text{ m/s}$.

A thin convex lens of focal length 5 cm and a thin concave lens of focal length 4 cm are combined together (without any gap) and this combination has magnification $m_1$ when an object is placed 10 cm before the convex lens. Keeping the positions of convex lens and object undisturbed a gap of 1 cm is introduced between the lenses by moving the concave lens away, which lead to a change in magnification of total lens system to $m_2$. The value of $\left| \frac{m_1}{m_2} \right|$ is ______.

Consider an equilateral prism (refractive index $\sqrt{2}$ ). A ray of light is incident on its one surface at a certain angle $i$. If the emergent ray is found to graze along the other surface then the angle of refraction at the incident surface is close to ______

A parallel beam of light travelling in air (refractive index 1.0) is incident on a convex spherical glass surface of radius of curvature 50 cm. Refractive index of glass is 1.5. The rays converge to a point at a distance $x\text{ cm}$ from the centre of the curvature of the spherical surface. The value of $x$ is ______ cm.

A circular disc has radius $R_1$ and thickness $T_1$. Another circular disc made of the same material has radius $R_2$ and thickness $T_2$. If the moment of inertia of both discs are same and $\frac{R_1}{R_2} = 2$ then $\frac{T_1}{T_2} = \frac{1}{\alpha}$. The value of $\alpha$ is ______.

A solid sphere of mass 5 kg and radius 10 cm is kept in contact with another solid sphere of mass 10 kg and radius 20 cm. The moment of inertia of this pair of spheres about the tangent passing through the point of contact is $\underline{\qquad}\ \text{kg}\cdot\text{m}^2$.

A cylindrical tube $AB$ of length $l$, closed at both ends contains an ideal gas of 1 mol having molecular weight $M$. The tube is rotated in a horizontal plane with constant angular velocity $\omega$ about an axis perpendicular to $AB$ and passing through the edge at end $A$, as shown in the figure. If $P_A$ and $P_B$ are the pressures at $A$ and $B$ respectively, then (Consider the temperature is same at all points in the tube)

Find the correct combination of $\mathrm{A}, \mathrm{B}, \mathrm{C}$ and D inputs which can cause the LED to glow.

The volume of an ideal gas increases 8 times and temperature becomes $(1/4)$th of initial temperature during a reversible change. If there is no exchange of heat in this process $(\Delta Q = 0)$ then identify the gas from the following options (Assuming the gases given in the options are ideal gases):

Match the LIST-I with LIST-II

Choose the correct answer from the options given below:

Two loudspeakers $(L_1$ and $L_2)$ are placed with a separation of 10 m, as shown in figure. Both speakers are fed with an audio input signal of same frequency with constant volume. A voice recorder, initially at point $A$, at equidistant to both loudspeakers, is moved by 25 m along the line $AB$ while monitoring the audio signal. The measured signal was found to undergo 10 cycles of minima and maxima during the movement. The frequency of the input signal is ______ Hz (Speed of sound in air is $324\text{ m/s}$ and $\sqrt{5} = 2.23$)