JEE Main 2024 Physics Paper: 9 Apr, Shift 1

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:

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

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 $\frac{A}{3}$ and the height is $d$, the capacitance of the arrangement is:

The equivalent resistance between A and B is:

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

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

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

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

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

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

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 $318.5\text{ km}$. From earth's surface to the orbit, the change in total mechanical energy of the ball is $x\frac{GM_e m}{21R_e}$. The value of $x$ is (take $R_e = 6370\text{ km})$:

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:

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

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

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

The energy equivalent of $1\text{ g}$ of substance is:

A star has $100\%$ helium composition. It starts to convert three ${}^{4}\text{He}$ into one ${}^{12}\text{C}$ via triple alpha process as ${}^{4}\text{He} + {}^{4}\text{He} + {}^{4}\text{He} \rightarrow {}^{12}\text{C} + \text{Q}$. The mass of the star is $2.0 \times 10^{32}\text{ kg}$ and it generates energy at the rate of $5.808 \times 10^{30}\text{ W}$. The rate of converting these ${}^{4}\text{He}$ to ${}^{12}\text{C}$ is $\text{n} \times 10^{42}\text{ s}^{-1}$, where $\text{n}$ is _________. [ Take, mass of ${}^{4}\text{He} = 4.0026\text{u}$, mass of ${}^{12}\text{C} = 12\text{u}$]

The position, velocity and acceleration of a particle executing simple harmonic motion are found to have magnitudes of $4\text{ m}, 2\text{ m s}^{-1}$ and $16\text{ m s}^{-2}$ at a certain instant. The amplitude of the motion is $\sqrt{x}\text{ m}$ where $x$ 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 string is wrapped around the rim of a wheel of moment of inertia $0.40\text{ kg m}^{2}$ and radius $10\text{ cm}$. The wheel is free to rotate about its axis. Initially the wheel is at rest. The string is now pulled by a force of $40\text{ N}$. The angular velocity of the wheel after $10\text{ s}$ is $x\text{ rad/s}$, where $x$ 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 emitting diode (LED) is fabricated using GaAs semiconducting material whose band gap is $1.42\text{ eV}$. The wavelength of light emitted from the LED 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 sample of 1 mole gas at temperature $T$ is adiabatically expanded to double its volume. If adiabatic constant for the gas is $\gamma = \frac{3}{2}$, then the work done by the gas in the process is:

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

The dimensional formula of latent heat is:

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

In a Young's double slit experiment, the intensity at a point is $\left(\frac{1}{4}\right)$th of the maximum intensity, the minimum distance of the point from the central maximum is _________ $\mu\text{m}$. (Given: $\lambda = 600\text{ nm},\ d = 1.0\text{ mm}, D = 1.0\text{ m}$)

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: