JEE Main 2024 Physics Paper: 30 Jan, Shift 2

An alternating voltage $V(t) = 220 \sin 100\pi t$ volt is applied to a purely resistive load of $50\ \Omega$. The time taken for the current to rise from half of the peak value to the peak value is:

A power transmission line feeds input power at $2.3\text{ kV}$ to a step down transformer with its primary winding having 3000 turns. The output power is delivered at $230\text{ V}$ by the transformer. The current in the primary of the transformer is $5\text{ A}$ and its efficiency is $90\%$. The winding of transformer is made of copper. The output current of transformer is _________ $A$.

An electron revolving in $n$th Bohr orbit has magnetic moment $\mu_n$. If $\mu_n \propto n^x$, the value of $x$ is

When a potential difference $V$ is applied across a wire of resistance $R$, it dissipates energy at a rate $W$. If the wire is cut into two halves and these halves are connected mutually parallel across the same supply, the energy dissipation rate will become:

Two resistances of $100\ \Omega$ and $200\ \Omega$ are connected in series with a battery of $4\text{ V}$ and negligible internal resistance. A voltmeter is used to measure voltage across $100\ \Omega$ resistance, which gives reading as $1\text{ V}$. The resistance of voltmeter must be _______ $\Omega$.

For the photoelectric effect, the maximum kinetic energy $(E_k)$ of the photoelectrons is plotted against the frequency $(v)$ of the incident photons as shown in figure. The slope of the graph gives

If the total energy transferred to a surface in time $t$ is $6.48 \times 10^{5}\text{ J}$, then the magnitude of the total momentum delivered to this surface for complete absorption will be:

Match List I with List II

Choose the correct answer from the options given below:

Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of $37^\circ$ with each other. When suspended in a liquid of density $0.7\text{ g/cm}^{3}$, the angle remains same. If density of material of the sphere is $1.4\text{ g/cm}^{3}$, the dielectric constant of the liquid is _______ $\left(\tan 37^\circ = \frac{3}{4}\right)$

A particle of charge '$-q$' and mass '$m$' moves in a circle of radius '$r$' around an infinitely long line charge of linear charge density '$+\lambda$'. Then time period will be given as:

(Consider $k$ as Coulomb's constant)

A simple pendulum is placed at a place where its distance from the earth's surface is equal to the radius of the earth. If the length of the string is $4\text{ m}$, then the time period of small oscillations will be __________ s. [take $g = \pi^2\text{ m s}^{-2}$]

Escape velocity of a body from earth is $11.2\text{ km/s}$. If the radius of a planet be one-third the radius of earth and mass be one-sixth that of earth, the escape velocity from the planet is:

Three blocks $A, B$ and $C$ are pulled on a horizontal smooth surface by a force of $80\text{ N}$ as shown in figure

The tensions T$1$ and T$2$ in the string are respectively:

A block of mass $m$ is placed on a surface having vertical cross-section given by $y = x^2/4$. If coefficient of friction is 0.5, the maximum height above the ground at which block can be placed without slipping is:

A current of $5\text{ A}$ flows in a square loop of side $1\text{ m}$ placed in air. The magnetic field at the centre of the loop is $X\sqrt{2} \times 10^{-7}\text{ T}$. The value of $X$ is _________.

In a nuclear fission reaction of an isotope of mass $M$, three similar daughter nuclei of same mass are formed. The speed of a daughter nucleus in terms of mass defect $\Delta M$ will be:

Projectiles A and B are thrown at angles of $45^\circ$ and $60^\circ$ with vertical respectively from top of a $400\text{ m}$ high tower. If their ranges and times of flight are same, the ratio of their speeds of projection $v_A : v_B$ is:

[Take $g = 10\text{ m s}^{-2}$]

In an experiment to measure the focal length $(f)$ of a convex lens, the magnitude of object distance $(x)$ and the image distance $(y)$ are measured with reference to the focal point of the lens. The $y\text{-}x$ plot is shown in figure.

The focal length of the lens is ________ $\text{cm}$.

Two discs of moment of inertia $I_1 = 4\text{ kg m}^{2}$ and $I_2 = 2\text{ kg m}^{2}$, about their central axes & normal to their planes, rotating with angular speeds $10\text{ rad/s}$ & $4\text{ rad/s}$ respectively are brought into contact face to face with their axes of rotation coincident. The loss in kinetic energy of the system in the process is _________ J.

In the given circuit, the voltage across load resistance (R${}_L$) is:

A big drop is formed by coalescing 1000 small identical drops of water. If $E_1$ be the total surface energy of 1000 small drops of water and $E_2$ be the surface energy of single big drop of water, then $E_1 : E_2$ is $x : 1$ where $x =$ ________.

If three moles of monoatomic gas $\left(\gamma = \frac{5}{3}\right)$ is mixed with two moles of a diatomic gas $\left(\gamma = \frac{7}{5}\right)$, the value of adiabatic exponent $\gamma$ for the mixture is

A block of ice at $-10^{\circ}\text{C}$ is slowly heated and converted to steam at $100^{\circ}\text{C}$. Which of the following curves represent the phenomenon qualitatively:

If mass is written as $m = k\mathrm{c}^{\mathrm{P}}G^{-1/2}h^{1/2}$ then the value of $P$ will be: (Constants have their usual meaning with $k$ a dimensionless constant)

If 50 Vernier divisions are equal to 49 main scale divisions of a traveling microscope and one smallest reading of main scale is $0.5\text{ mm}$, the Vernier constant of traveling microscope is

A vector has magnitude same as that of $\vec{A} = 3\hat{i} + 4\hat{j}$ and is parallel to $\vec{B} = 4\hat{i} + 3\hat{j}$. The $x$ and $y$ components of this vector in first quadrant are $x$ and 3 respectively where $x =$ _________.

A point source is emitting sound waves of intensity $16 \times 10^{-8}\text{ Wm}^{-2}$ at the origin. The difference in intensity (magnitude only) at two points located at distances of $2\text{ m}$ and $4\text{ m}$ from the origin respectively will be _________ $\times 10^{-8}\text{ Wm}^{-2}$.

A beam of unpolarised light of intensity $I_0$ is passed through a polaroid $A$ and then through another polaroid $B$ which is oriented so that its principal plane makes an angle of $45^\circ$ relative to that of $A$. The intensity of emergent light is:

A block of mass $1\text{ kg}$ is pushed up a surface inclined to horizontal at an angle of $60^\circ$ by a force of $10\text{ N}$ parallel to the inclined surface as shown in figure. When the block is pushed up by $10\text{ m}$ along inclined surface, the work done against frictional force is:

$\left[g = 10\text{ m/s}^2\right]$