JEE Main 2026 Apr 6 Shift 1 — Physics

The density $\rho$ of a uniform cylinder is determined by measuring its mass $m$, length $l$ and diameter $d$. The measured values of $m$, $l$ and $d$ are $97.42 \pm 0.02$ g, $8.35 \pm 0.05$ mm and $20.20 \pm 0.02$ mm, respectively. Calculated percentage fractional error in $\rho$ is ________.

The potential energy of a particle changes with distance $x$ from a fixed origin as $V = \frac{A\sqrt{x}}{x + B}$, where $A$ and $B$ are constant with appropriate dimensions. The dimensions of $AB$ are ________.

The rain drop of mass 1 g, starts with zero velocity from a height of 1 km. It hits the ground with a speed of 5 m/s. The work done by the unknown resistive force is ________ J.

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

Two blocks ($P$ and $Q$) with respectively masses 2 kg and 1.5 kg are joined by a massless thread. These blocks are mounted on a frictionless pully which is fixed on the edge of a cube ($S$), as shown in the figure below. Block $P$ is positioned on the top surface which has no friction and block $Q$ is in contact with side-surface, having coefficient friction $\mu$. The cube ($S$) moves towards the right with acceleration of $\frac{g}{2}$, where $g$ is gravitational acceleration. During this movement the block $P$ and $Q$ remain stationary. The value of $\mu$ is ________.

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

A cube $S$ with block $P$ (2 kg) on its top surface connected over a pulley at the top edge to block $Q$ (1.5 kg) hanging against the right side-surface of the cube

A lift of mass 1600 kg is supported by thick iron wire. If the maximum stress which the wire can withstand is $4 \times 10^{8}\ \text{N/m}^2$ and its radius is 4 mm, then maximum acceleration the lift can take is ______ $\text{m/s}^2$.

(take $g = 10\ \text{m/s}^2$ and $\pi = 3.14$)

A solid sphere of radius 4 cm and mass 5 kg is rotating (rotation axis is passing through the centre of the sphere) with an angular velocity of 1200 rpm. It is brought to rest in 10 s by applying a constant torque. The torque applied and the number of rotations it made before it comes to rest are ______ and ________ respectively.

A smooth inclined plane ends in a vertical circular loop, as shown in the figure. A small body is released from height $h$ as shown. If the body exerts a force of three times its weight on the plane at the highest point of circle then the height $h = \alpha R$. The value of $\alpha$ is ________.

An inclined plane of height $h$ leading down to a vertical circular loop of radius $R$ at its base

The position of center of mass of three masses 2 kg, 3 kg and 15 kg placed with respect to mid point ($p$) of normal bisector, as shown in the figure is ________.

An isosceles triangle arrangement: 2 kg at the left base corner, 3 kg at the right base corner, and 15 kg at the apex; the two slant sides are 10 m each with $120°$ angle at the apex; point $p$ is the midpoint of the normal bisector from the apex to the base

The two wires $A$ and $B$ of equal cross-section but of different materials are joined together. The ratio of Young's modulus of wire $A$ and wire $B$ is $20/11$. When the joined wire is kept under certain tension the elongations in the wires $A$ and $B$ are equal. If the length of wire $A$ is 2.2 m, then the length of wire $B$ is ________ m.

Two closed vessels of same volume are joined through a narrow tube and both vessels are filled with air of pressure 90 kPa and temperature 400 K. Keeping the temperature of one vessel constant at 400 K the second vessel temperature is raised to 500 K. The final pressure in the vessels is ________ kPa.

In interference experiment the path difference between two interfering waves at a point $A$ on the screen is $\lambda/3$, where $\lambda$ is the wavelength of these waves, and at another point $B$ the path difference is $\lambda/6$. The ratio of intensities at points $A$ and $B$ is ________.

A particle is executing simple harmonic motion. Its amplitude is $A$ and time period is 5 sec. The time required by it to move from $x = A$ to $x = \frac{A}{\sqrt{2}}$ is ________ sec.

A thin half ring of radius 35 cm is uniformly charged with a total charge of $Q$ coulomb. If the magnitude of the electric field at centre of the half ring is 100 V/m, then the value of $Q$ is ________ nC.

($\epsilon_o = 8.85 \times 10^{-12}\ \text{C}^2/\text{Nm}^2$ and $\pi = 3.14$)

The maximum rated power of the LED is 2 mW and it is used in the circuit with input voltage of 5 V as shown in the figure below. The current through resistance $R_S$ is 0.5 mA.

The minimum value of the resistance of $R_S$, to ensure that the LED is not damaged is ________ $\text{k}\Omega$.

A 5 V source in series with resistance $R_S$; the circuit then splits into two parallel branches: one with $R = 1\ \text{k}\Omega$ in series with a diode, and the other with a 2 mW LED

A point light source emits E.M. waves in free space. A detector, placed at a distance of $L$ m, measures the intensity as $I_o$. The detector is now shifted to another location on the same spherical surface ensuring the angle between original location and new location as $45°$. The measured intensity at new location will be ________.

A spherical interface lens of radius $R$ separates two media of refractive indices 1 and 1.4 respectively as shown in the figure below. A point source is placed at a distance of $4R$ in front of spherical interface. The magnitude of the magnification of point source image is ________.

A point source $p$ on the axis at distance $4R$ to the left of a convex spherical interface of radius $R$; medium on the left has $n_1 = 1$ and medium on the right has $n_2 = 1.4$

A small cube of side 1 mm is placed at the centre of a circular loop of radius 10 cm carrying a current of 2 A. The magnetic energy stored inside the cube is $\alpha \times 10^{-14}$ J. The value of $\alpha$ is ________.

($\mu_o = 4\pi \times 10^{-7}\ \text{Tm/A}$, $\pi = 3.14$)

An inductor of inductance 10 mH having resistance of 100 $\Omega$ is connected to battery of E.M.F. 1.0 V through a switch as shown in the figure below. After switch is closed, the ratio of instantaneous voltages across the inductor when the current passing through it is 2 mA and 4 mA is ________.

A series circuit with an inductor, a battery, and an open switch

The ratio of momentum of the photons of the $1^{\text{st}}$ and $2^{\text{nd}}$ line of Balmer series of Hydrogen atoms is $\alpha/\beta$. The possible values of $\alpha$ and $\beta$ are:-

A LCR series circuit driven with $E_{rms} = 90$ V at frequency $f_d = 30$ Hz has resistance $R = 80\ \Omega$, an inductance with inductive reactance $X_L = 20.0\ \Omega$ and capacitance with capacitive reactance $X_C = 80.0\ \Omega$. The power factor of the circuit is ______.

Refer to the circuit diagram given below. The heat generated across the 6 $\Omega$ resistance in 100 second is $\frac{\alpha}{100}$ J. The value of $\alpha$ is ________. (Nearest integer)

A circuit with two loops: the upper branch has a 6 $\Omega$ resistor in series with a 3 V battery; a parallel branch has a 4 $\Omega$ resistor; the outer loop contains a 3 $\Omega$ resistor and a 2 V battery

An unpolarized light of intensity $I_o$ passes through polarizer and then through a certain optically active solution and finally it goes to analyser. If the angle between analyser and polariser is $0°$ and intensity of light emerged from analyser is $\frac{3}{8} I_o$, the angle of rotation of the light by the solution with respect to analyser is ______ degrees.

The energy released when $\frac{7}{17.13}$ kg of $^{7}_{3}\text{Li}$ is converted into $^{4}_{2}\text{He}$ by proton bombardment is $\alpha \times 10^{32}$ eV. The value of $\alpha$ is ____. (Nearest integer)

(Mass of $^{7}_{3}\text{Li} = 7.0183$ u, mass of $^{4}_{2}\text{He} = 4.004$ u, mass of proton $= 1.008$ u and $1\ \text{u} = 931\ \text{MeV/c}^2$ and Avogadro number $= 6.0 \times 10^{23}$)

A three coulomb charge moves from the point $(0, -2, -5)$ to the point $(5, 1, 2)$ in an electric field expressed as $\vec{E} = 2x\hat{i} + 3y^2\hat{j} + 4\hat{k}$ N/C. The work done in moving the charge is ______ J.

A certain gas is isothermally compressed to $\left(\frac{1}{3}\right)^{\text{rd}}$ of its initial volume ($V_o = 3$ litre) by applying required pressure. If the bulk modulus of the gas is $3 \times 10^{5}\ \text{N/m}^2$, the magnitude of work done on the gas is _____ J.