JEE Main 2023 Physics Paper: 8 Apr, Shift 1

An oscillating LC circuit consists of a $75\text{ mH}$ inductor and a $1.2\,\mu\text{F}$ capacitor. If the maximum charge to the capacitor is $2.7\,\mu\text{C}$. The maximum current in the circuit will be ___________ $\text{mA}$

In this figure the resistance of the coil of galvanometer G is $2\ \Omega$. The emf of the cell is $4\text{ V}$. The ratio of potential difference across $C_1$ and $C_2$ is:

A current of $2\text{ A}$ flows through a wire of cross-sectional area $25.0\text{ mm}^{2}$. The number of free electrons in a cubic meter are $2.0 \times 10^{28}$. The drift velocity of the electrons is __________ $\times 10^{-6}\text{ m s}^{-1}$ (given, charge on electron $= 1.6 \times 10^{-19}\text{ C}$ ).

Proton $(\mathrm{P})$ and electron (e) will have same de-Broglie wavelength when the ratio of their momentum is (assume, $\mathrm{m_p} = 1849\, \mathrm{m_e}$ ):

Certain galvanometers have a fixed core made of non magnetic metallic material. The function of this metallic material is

An electric dipole of dipole moment $6.0 \times 10^{-6}\text{ Cm}$ is placed in a uniform electric field of $1.5 \times 10^{3}\text{ NC}^{-1}$ in such a way that dipole moment is along electric field. The work done in rotating dipole by $180^\circ$ in this field will be ___________ $\text{mJ}$.

Graphical variation of electric field due to a uniformly charged insulating solid sphere of radius $R$, with distance $r$ from the centre O is represented by:

An air bubble of volume $1\text{ cm}^{3}$ rises from the bottom of a lake $40\text{ m}$ deep to the surface at a temperature of $12^\circ\text{C}$. The atmospheric pressure is $1 \times 10^{5}\text{ Pa}$ the density of water is $1000\text{ kg/m}^{3}$ and $g = 10\text{ m/s}^{2}$. There is no difference of the temperature of water at the depth of $40\text{ m}$ and on the surface. The volume of air bubble when it reaches the surface will be:

The weight of a body on the earth is $400\text{ N}$. Then weight of the body when taken to a depth half of the radius of the earth will be:

Given below are two statements:

Statement I: If $E$ be the total energy of a satellite moving around the earth, then its potential energy will be $\frac{E}{2}$.

Statement II: The kinetic energy of a satellite revolving in an orbit is equal to the half the magnitude of total energy $E$.

In the light of the above statements, choose the most appropriate answer from the options given below

At any instant the velocity of a particle of mass $500\text{ g}$ is $\left(2t\hat{i} + 3t^2\hat{j}\right)\text{ m s}^{-1}$. If the force acting on the particle at $t = 1\text{ s}$ is $(\hat{i} + x\hat{j})\text{ N}$. Then the value of $x$ will be:

The magnetic intensity at the center of a long current carrying solenoid is found to be $1.6 \times 10^{3}\text{ Am}^{-1}$. If the number of turns is 8 per cm, then the current flowing through the solenoid is __________ A.

An aluminium rod with Young's modulus $Y = 7.0 \times 10^{10}\text{ N/m}^2$ undergoes elastic strain of $0.04\%$. The energy per unit volume stored in the rod in SI unit is:

A charge particle moving in magnetic field B, has the components of velocity along B as well as perpendicular to B. The path of the charge particle will be

For a nucleus ${}_{\text{Z}}^{\text{A}}\text{X}$ having mass number $\text{A}$ and atomic number $\text{Z}$

A. The surface energy per nucleon $(b_{\text{s}}) = -a_1 A^{2/3}$.

B. The Coulomb contribution to the binding energy $\text{b}_{\text{c}} = -a_2 \frac{Z(Z-1)}{A^{4/3}}$

C. The volume energy $\text{b}_{\text{v}} = a_3 A$

D. Decrease in the binding energy is proportional to surface area.

E. While estimating the surface energy, it is assumed that each nucleon interacts with 12 nucleons. ( $a_1, a_2$ and $a_3$ are constants)

Choose the most appropriate answer from the options given below:

A nucleus with mass number 242 and binding energy per nucleon as $7.6\text{ MeV}$ breaks into two fragment each with mass number 121. If each fragment nucleus has binding energy per nucleon as $8.1\text{ MeV}$, the total gain in binding energy is _________ $\text{MeV}$.

Two projectiles A and B are thrown with initial velocities of $40\text{ m/s}$ and $60\text{ m/s}$ at angles $30^\circ$ and $60^\circ$ with the horizontal respectively. The ratio of their ranges respectively is $\left(g = 10\text{ m/s}^{2}\right)$

In a reflecting telescope, a secondary mirror is used to:

Two vertical parallel mirrors A and B are separated by $10\text{ cm}$. A point object $\text{O}$ is placed at a distance of $2\text{ cm}$ from mirror $\text{A}$. The distance of the second nearest image behind mirror A from the mirror $\text{A}$ is _________ $\text{cm}$.

The moment of inertia of a semicircular ring about an axis, passing through the center and perpendicular to the plane of ring, is $\frac{1}{x}MR^2$, where $R$ is the radius and $M$ is the mass of the semicircular ring. The value of $x$ will be __________.

For the logic circuit shown, the output waveform at $\mathrm{Y}$ is:

Given below are two statements:

Statement I: If heat is added to a system, its temperature must increase.

Statement II: If positive work is done by a system in a thermodynamic process, its volume must increase.

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

A cylindrical wire of mass $(0.4 \pm 0.01)\text{ g}$ has length $(8 \pm 0.04)\text{ cm}$ and radius $(6 \pm 0.03)\text{ mm}$. The maximum error in its density will be:

Dimension of $\frac{1}{\mu_0\epsilon_0}$ should be equal to

Two forces having magnitude $A$ and $\frac{A}{2}$ are perpendicular to each other. The magnitude of their resultant is:

An air bubble of diameter $6\text{ mm}$ rises steadily through a of density $1750\text{ kg/m}^{3}$ at the rate of $0.35\text{ cm/s}$. The co-efficient of viscosity of the (neglect density of air) is ___________ Pas (given, $\mathrm{g} = 10\text{ ms}^{-2}$ ).

The engine of a train moving with speed $10\text{ ms}^{-1}$ towards a platform sounds a whistle at frequency $400\text{ Hz}$. The frequency heard by a passenger inside the train is: (neglect air speed. Speed of sound in air $= 330\text{ ms}^{-1}$)

An organ pipe $40\text{ cm}$ long is open at both ends. The speed of sound in air is $360\text{ ms}^{-1}$. The frequency of the second harmonic is ___________ $\text{Hz}$.