JEE Main 2024 Apr 9 Shift 1 — Physics

The dimensional formula of latent heat is :

A particle moving in a straight line covers half the distance with speed 6 m/s. The other half is covered in two equal time intervals with speeds 9 m/s and 15 m/s respectively. The average speed of the particle during the motion is :

A heavy iron bar, of weight W is having its one end on the ground and the other on the shoulder of a person. The bar makes an angle $\theta$ with the horizontal. The weight experienced by the person is :

A light unstretchable string passing over a smooth light pulley connects two blocks of masses $m_1$ and $m_2$. If the acceleration of the system is $\frac{g}{8}$, then the ratio of the masses $\frac{m_2}{m_1}$ is :

A particle of mass m moves on a straight line with its velocity increasing with distance according to the equation $v = \alpha\sqrt{x}$, where $\alpha$ is a constant. The total work done by all the forces applied on the particle during its displacement from $x = 0$ to $x = d$, will be :

An astronaut takes a ball of mass m from earth to space. He throws the ball into a circular orbit about earth at an altitude of 318.5 km. From earth's surface to the orbit, the change in total mechanical energy of the ball is $x\dfrac{GM_e m}{21R_e}$. The value of $x$ is (take $R_e = 6370$ km) :

A sphere of relative density $\sigma$ and diameter D has concentric cavity of diameter d. The ratio of $\dfrac{D}{d}$, if it just floats on water in a tank is :

A sample of 1 mole gas at temperature T is adiabatically expanded to double its volume. If adiabatic constant for the gas is $\gamma = \dfrac{3}{2}$, then the work done by the gas in the process is :

The volume of an ideal gas ($\gamma = 1.5$) is changed adiabatically from 5 litres to 4 litres. The ratio of initial pressure to final pressure is :

A capacitor is made of a flat plate of area A and a second plate having a stair-like structure as shown in figure. If the area of each stair is $\dfrac{A}{3}$ and the height is d, the capacitance of the arrangement is :

a flat bottom plate of area A; above it a stair-like top plate with three steps each of area A/3, at heights d, 2d and 3d from the bottom plate

The equivalent resistance between A and B is :

resistor network between terminals A and B: top row has 6 Ω and 10 Ω in series; left side has 8 Ω and 4 Ω; right side has 5 Ω and 7 Ω; bottom row has 11 Ω and 8 Ω in series; a middle vertical branch crosses over the horizontal middle wire

Given below are two statements :

Statement (I) : When currents vary with time, Newton's third law is valid only if momentum carried by the electromagnetic field is taken into account.

Statement (II) : Ampere's circuital law does not depend on Biot-Savart's law.

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

A bulb and a capacitor are connected in series across an ac supply. A dielectric is then placed between the plates of the capacitor. The glow of the bulb :

A plane EM wave is propagating along $x$ direction. It has a wavelength of 4 mm. If electric field is in $y$ direction with the maximum magnitude of $60\ \mathrm{Vm^{-1}}$, the equation for magnetic field is :

Given below are two statements :

Statement (I) : When an object is placed at the centre of curvature of a concave lens, image is formed at the centre of curvature of the lens on the other side.

Statement (II) : Concave lens always forms a virtual and erect image.

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

A proton, an electron and an alpha particle have the same energies. Their de-Broglie wavelengths will be compared as :

The energy equivalent of 1 g of substance is :

A light emitting diode (LED) is fabricated using GaAs semiconducting material whose band gap is 1.42 eV. The wavelength of light emitted from the LED is :

One main scale division of a vernier caliper is equal to m units. If $n^{\text{th}}$ division of main scale coincides with $(n+1)^{\text{th}}$ division of vernier scale, the least count of the vernier caliper is :

A galvanmeter has a coil of resistance $200\ \Omega$ with a full scale deflection at $20\ \mu\mathrm{A}$. The value of resistance to be added to use it as an ammeter of range (0-20) mA is :

If $\vec{a}$ and $\vec{b}$ makes an angle $\cos^{-1}\left(\dfrac{5}{9}\right)$ with each other, then $\left|\vec{a} + \vec{b}\right| = \sqrt{2}\left|\vec{a} - \vec{b}\right|$ for $\left|\vec{a}\right| = n\left|\vec{b}\right|$. The integer value of n is ________.

A string is wrapped around the rim of a wheel of moment of inertia $0.40\ \mathrm{kgm^2}$ and radius 10 cm. The wheel is free to rotate about its axis. Initially the wheel is at rest. The string is now pulled by a force of 40 N. The angular velocity of the wheel after 10 s is $x$ rad/s, where $x$ is ________.

Two persons pull a wire towards themselves. Each person exerts a force of 200 N on the wire. Young's modulus of the material of wire is $1 \times 10^{11}\ \mathrm{N\,m^{-2}}$. Original length of the wire is 2 m and the area of cross section is $2\ \mathrm{cm^2}$. The wire will extend in length by ________ $\mu\mathrm{m}$.

The position, velocity and acceleration of a particle executing simple harmonic motion are found to have magnitudes of 4 m, $2\ \mathrm{ms^{-1}}$ and $16\ \mathrm{ms^{-2}}$ at a certain instant. The amplitude of the motion is $\sqrt{x}$ m where $x$ is ________.

At the centre of a half ring of radius $R = 10$ cm and linear charge density $4\ \mathrm{nC\ m^{-1}}$, the potential is $x\pi$ V. The value of $x$ is ________.

The current flowing through the $1\ \Omega$ resistor is $\dfrac{n}{10}$ A. The value of n is ________.

diamond-shaped circuit A-B-C-D-E: a 10 V battery with 4 Ω and 1 Ω resistors on branch A to C (current I₁ marked through the 1 Ω), a 2 Ω resistor from B to C and another 2 Ω from C to D, 4 Ω on branch A to D, and a 5 V battery at E on the right connecting B and D

A square loop of edge length 2 m carrying current of 2 A is placed with its edges parallel to the $x$-$y$ axis. A magnetic field is passing through the $x$-$y$ plane and expressed as $\vec{B} = B_0(1 + 4x)\hat{k}$, where $B_0 = 5$ T. The net magnetic force experienced by the loop is ________ N.

When a coil is connected across a 20 V dc supply, it draws a current of 5 A. When it is connected across 20 V, 50 Hz ac supply, it draws a current of 4 A. The self inductance of the coil is ________ mH. (Take $\pi = 3$)

In a Young's double slit experiment, the intensity at a point is $\left(\dfrac{1}{4}\right)^{\text{th}}$ of the maximum intensity, the minimum distance of the point from the central maximum is ________ $\mu\mathrm{m}$.

(Given : $\lambda = 600$ nm, $d = 1.0$ mm, $D = 1.0$ m)

A star has 100% helium composition. It starts to convert three $^{4}\mathrm{He}$ into one $^{12}\mathrm{C}$ via triple alpha process as $^{4}\mathrm{He} + {}^{4}\mathrm{He} + {}^{4}\mathrm{He} \rightarrow {}^{12}\mathrm{C} + Q$. The mass of the star is $2.0 \times 10^{32}$ kg and it generates energy at the rate of $5.808 \times 10^{30}$ W. The rate of converting these $^{4}\mathrm{He}$ to $^{12}\mathrm{C}$ is $n \times 10^{42}\ \mathrm{s^{-1}}$, where n is ________.

[ Take, mass of $^{4}\mathrm{He} = 4.0026$ u, mass of $^{12}\mathrm{C} = 12$ u]