JEE Main 2023 Physics Paper: 31 Jan, Shift 2

An alternating voltage source $V = 260 \sin(628t$) is connected across a pure inductor of $5\text{ mH}$. Inductive reactance in the circuit is:

A series $LCR$ circuit consists of $R = 80\ \Omega, X_L = 100\ \Omega$, and $X_C = 40\ \Omega$. The input voltage is 2500 $\cos(100\pi t)\text{ V}$. The amplitude of current, in the circuit, is _________ A.

The radius of electron's second stationary orbit in Bohr's atom is R. The radius of 3rd orbit will be

If the binding energy of ground state electron in a hydrogen atom is $13.6\text{ eV}$, then, the energy required to remove the electron from the second excited state of $\text{Li}^{2+}$ will be: $x \times 10^{-1}\text{ eV}$. The value of $x$ is ________.

For the given circuit, in the steady state, $|V_B-V_D|=$ ________ V.

Two parallel plate capacitors $C_1$ and $C_2$ each having capacitance of $10\ \mu\text{F}$ are individually charged by a 100 V D.C. source. Capacitor $C_1$ is kept connected to the source and a dielectric slab is inserted between its plates. Capacitor $C_2$ is disconnected from the source and then a dielectric slab is inserted in it. Afterwards the capacitor $C_1$ is also disconnected from the source and the two capacitors are finally connected in parallel combination. The common potential of the combination will be ________ V.

(Assuming Dielectric constant $= 10$)

A body is moving with constant speed, in a circle of radius $10\text{ m}$. The body completes one revolution in $4\text{ s}$. At the end of 3rd second, the displacement of body (in $\text{m}$) from its starting point is:

A stone of mass $1\text{ kg}$ is tied to end of a massless string of length $1\text{ m}$. If the breaking tension of the string is $400\text{ N}$, then maximum linear velocity, the stone can have without breaking the string, while rotating in horizontal plane, is:

The $\mathrm{H}$ amount of thermal energy is developed by a resistor in $10\text{ s}$ when a current of $4\text{ A}$ is passed through it. If the current is increased to $16\text{ A}$, the thermal energy developed by the resistor in $10\text{ s}$ will be:

The number of turns of the coil of a moving coil galvanometer is increased in order to increase current sensitivity by $50\%$. The percentage change in voltage sensitivity of the galvanometer will be:

If the two metals $\text{A}$ and $\text{B}$ are exposed to radiation of wavelength $350\text{ nm}$. The work functions of metals $\text{A}$ and $\text{B}$ are $4.8\text{ eV}$ and $2.2\text{ eV}$. Then choose the correct option.

Match List I with List II

Choose the correct answer from the options given below:

Considering a group of positive charges, which of the following statements is correct?

A body weight $W$, is projected vertically upwards from earth's surface to reach a height above the earth which is equal to nine times the radius of earth. The weight of the body at that height will be:

A body of mass $10\text{ kg}$ is moving with an initial speed of $20\text{ m/s}$. The body stops after $5\text{ s}$ due to friction between body and the floor. The value of the coefficient of friction is:

(Take acceleration due to gravity $g = 10\text{ ms}^{-2}$)

For a solid rod, the Young's modulus of elasticity is $3.2 \times 10^{11}\text{ N m}^{-2}$ and density is $8 \times 10^{3}\text{ kg m}^{-3}$. The velocity of longitudinal wave in the rod will be.

Under the same load, wire A having length $5.0\text{ m}$ and cross section $2.5 \times 10^{-5}\text{ m}^2$ stretches uniformly by the same amount as another wire B of length $6.0\text{ m}$ and a cross section of $3.0 \times 10^{-5}\text{ m}^2$ stretches. The ratio of the Young's modulus of wire A to that of wire $B$ will be:

A long conducting wire having a current I flowing through it, is bent into a circular coil of $N$ turns. Then it is bent into a circular coil of $n$ turns. The magnetic field is calculated at the centre of coils in both the cases. The ratio of the magnetic field in first case to that of second case is:

Two bodies are projected from ground with same speeds $40\text{ m s}^{-1}$ at two different angles with respect to horizontal. The bodies were found to have same range. If one of the body was projected at an angle of $60^\circ$, with horizontal then sum of the maximum heights, attained by the two projectiles, is ________ $\text{m}$. (Given $g = 10\text{ m s}^{-2}$)

A microscope is focused on an object at the bottom of a bucket. If liquid with refractive index $\frac{5}{3}$ is poured inside the bucket, then the microscope has to be raised by $30\text{ cm}$ to focus the object again. The height of the liquid in the bucket is:

Two discs of same mass and different radii are made of different materials such that their thicknesses are $1\text{ cm}$ and $0.5\text{ cm}$ respectively. The densities of materials are in the ratio $3:5$. The moment of inertia of these discs respectively about their diameters will be in the ratio of $\frac{x}{6}$. The value of $x$ is ________.

Given below are two statements:

Statement I: In a typical transistor, all three regions emitter, base and collector have same doping level.

Statement II: In a transistor, collector is the thickest and base is the thinnest segment. In the light of the above statements, choose the most appropriate answer from the options given below.

Heat energy of $735\text{ J}$ is given to a diatomic gas allowing the gas to expand at constant pressure. Each gas molecule rotates around an internal axis but do not oscillate. The increase in the internal energy of the gas will be:

A hypothetical gas expands adiabatically such that its volume changes from 8 litres to 27 litres. If the ratio of final pressure of the gas to initial pressure of the gas is $\frac{16}{81}$. Then the ratio of $\frac{C_p}{C_v}$ will be.

A water heater of power $2000\text{ W}$ is used to heat water. The specific heat capacity of water is $4200\text{ J kg}^{-1}\text{ K}^{-1}$. The efficiency of heater is $70\%$. Time required to heat $2\text{ kg}$ of water from $10^{\circ}\text{C}$ to $60^{\circ}\text{C}$ is _________ s.

(Assume that the specific heat capacity of water remains constant over the temperature range of the water).

Match List I with List II

Choose the correct answer from the options given below:

The displacement equations of two interfering waves are given by

$y_1 = 10\sin\left(\omega t + \frac{\pi}{3}\right)\text{ cm}, y_2 = 5[\sin\omega t + \sqrt{3}\cos\omega t]\text{ cm}$ respectively.

The amplitude of the resultant wave is _______ $\text{cm}$.

Two light waves of wavelengths 800 and $600\text{ nm}$ are used in Young's double slit experiment to obtain interference fringes on a screen placed $7\text{ m}$ away from plane of slits. If the two slits are separated by $0.35\text{ mm}$, then shortest distance from the central bright maximum to the point where the bright fringes of the two wavelength coincide will be ______ $\text{mm}$.