JEE Main 2024 Physics Paper: 6 Apr, Shift 2

For a given series LCR circuit it is found that maximum current is drawn when value of variable capacitance is $2.5\text{ nF}$. If resistance of $200\ \Omega$ and $100\text{ mH}$ inductor is being used in the given circuit. The frequency of ac source is _________ $\times 10^{3}\text{ Hz}$ (given $\pi^2 = 10$)

The longest wavelength associated with Paschen series is: (Given $R_H = 1.097 \times 10^{7}\text{ SI}$ unit)

A capacitor of $10\ \mu\text{F}$ capacitance whose plates are separated by $10\text{ mm}$ through air and each plate has area $4\text{ cm}^2$ is now filled equally with two dielectric media of $K_1 = 2, K_2 = 3$ respectively as shown in figure. If new force between the plates is $8\text{ N}$. The supply voltage is ________ V.

A car of $800\text{ kg}$ is taking turn on a banked road of radius $300\text{ m}$ and angle of banking $30^\circ$. If coefficient of static friction is 0.2 then the maximum speed with which car can negotiate the turn safely: $(g = 10\text{ m/s}^2, \sqrt{3} = 1.73)$

The number of electrons flowing per second in the filament of a $110\text{ W}$ bulb operating at $220\text{ V}$ is: (Given $\text{e} = 1.6 \times 10^{-19}\text{ C}$)

In the given figure an ammeter A consists of a $240\ \Omega$ coil connected in parallel to a $10\ \Omega$ shunt. The reading of the ammeter is ________ $\text{mA}$.

In Franck-Hertz experiment, the first dip in the current-voltage graph for hydrogen is observed at $10.2\text{ V}$. The wavelength of light emitted by hydrogen atom when excited to the first excitation level is ________ nm. (Given hc $= 1245\text{ eV nm},\ e = 1.6 \times 10^{-19}\text{ C}$).

When UV light of wavelength $300\text{ nm}$ is incident on the metal surface having work function $2.13\text{ eV}$, electron emission takes place. The stopping potential is:

(Given hc $= 1240\text{ eV nm}$)

In a coil, the current changes from $-2\text{ A}$ to $+2\text{ A}$ in $0.2\text{ s}$ and induces an emf of $0.1\text{ V}$. The self inductance of the coil is:

In the given electromagnetic wave $E_y = 600 \sin(\omega t - kx)\text{ V m}^{-1}$, intensity of the associated light beam is (in $\text{W/m}^2$): (Given $\epsilon_0 = 9 \times 10^{-12}\text{ C}^2\text{ N}^{-1}\text{ m}^{-2}$)

Two identical conducting spheres P and S with charge Q on each, repel each other with a force $16\text{ N}$. A third identical uncharged conducting sphere $R$ is successively brought in contact with the two spheres. The new force of repulsion between $P$ and $S$ is:

Assuming the earth to be a sphere of uniform mass density, a body weighed $300\text{ N}$ on the surface of earth. How much it would weigh at R/4 depth under surface of earth?

A body of weight $200\text{ N}$ is suspended from a tree branch through a chain of mass $10\text{ kg}$. The branch pulls the chain by a force equal to (if $g = 10\text{ m/s}^2$):

A wire of cross sectional area A, modulus of elasticity $2 \times 10^{11}\text{ Nm}^{-2}$ and length $2\text{ m}$ is stretched between two vertical rigid supports. When a mass of $2\text{ kg}$ is suspended at the middle it sags lower from its original position making angle $\theta = \frac{1}{100}$ radian on the points of support. The value of A is ________ $\times 10^{-4}\text{ m}^2$ (consider $x << \text{L}$ ).

(given: $\text{g} = 10\text{ m/s}^2$)

A body projected vertically upwards with a certain speed from the top of a tower reaches the ground in $t_1$. If it is projected vertically downwards from the same point with the same speed, it reaches the ground in $t_2$. Time required to reach the ground, if it is dropped from the top of the tower, is:

A particle moves in a straight line so that its displacement $x$ at any time $t$ is given by $x^2 = 1 + t^2$. Its acceleration at any time $t$ is $x^{-n}$ where $n =$ _________.

A coil having 100 turns, area of $5 \times 10^{-3}\text{ m}^{2}$, carrying current of $1\text{ mA}$ is placed in uniform magnetic field of $0.20\text{ T}$ such a way that plane of coil is perpendicular to the magnetic field. The work done in turning the coil through $90^\circ$ is _________ $\mu\text{J}$.

For the thin convex lens, the radii of curvature are at $15\text{ cm}$ and $30\text{ cm}$ respectively. The focal length of the lens is $20\text{ cm}$. The refractive index of the material is:

Three balls of masses $2\text{ kg}, 4\text{ kg}$ and $6\text{ kg}$ respectively are arranged at centre of the edges of an equilateral triangle of side $2\text{ m}$. The moment of inertia of the system about an axis through the centroid and perpendicular to the plane of triangle, will be ________ $\text{kg m}^2$.

The acceptor level of a p-type semiconductor is $6\text{ eV}$. The maximum wavelength of light which can create a hole would be: Given $hc = 1242\text{ eV nm}$.

Pressure inside a soap bubble is greater than the pressure outside by an amount: (given: $R =$ Radius of bubble, $S =$ Surface tension of bubble)

Energy of 10 non rigid diatomic molecules at temperature $T$ is:

A total of $48\text{ J}$ heat is given to one mole of helium kept in a cylinder. The temperature of helium increases by $2^\circ\text{C}$. The work done by the gas is: Given, $R = 8.3\text{ J K}^{-1}\text{ mol}^{-1}$.

In a vernier calliper, when both jaws touch each other, zero of the vernier scale shifts towards left and its $4$th division coincides exactly with a certain division on main scale. If 50 vernier scale divisions equal to 49 main scale divisions and zero error in the instrument is $0.04\text{ mm}$ then how many main scale divisions are there in $1\text{ cm}$?

In finding out refractive index of glass slab the following observations were made through travelling microscope 50 vernier scale division $= 49\text{ MSD};\ 20$ divisions on main scale in each $\text{cm}$ For mark on paper

MSR $= 8.45\text{ cm},\ \text{VC} = 26$

For mark on paper seen through slab

$\text{MSR} = 7.12\text{ cm},\ \text{VC} = 41$

For powder particle on the top surface of the glass slab

MSR $= 4.05\text{ cm},\ \text{VC} = 1$

(MSR $=$ Main Scale Reading, VC = Vernier Coincidence)

Refractive index of the glass slab is:

Given below are two statements:

Statement (I): Dimensions of specific heat is $[\mathrm{L^{2}T^{-2}K^{-1}}]$.

Statement (II): Dimensions of gas constant is $[\mathrm{ML^{2}T^{-1}K^{-1}}]$.

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

Two open organ pipes of lengths $60\text{ cm}$ and $90\text{ cm}$ resonate at $6$th and $5$th harmonics respectively. The difference of frequencies for the given modes is _________ $\text{Hz}$. (Velocity of sound in air $= 333\text{ m/s}$)

Two coherent monochromatic light beams of intensities I and $4I$ are superimposed. The difference between maximum and minimum possible intensities in the resulting beam is $xI$. The value of $x$ is __________.

When kinetic energy of a body becomes 36 times of its original value, the percentage increase in the momentum of the body will be: