JEE Main 2024 Apr 6 Shift 2 — Physics

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

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 $[\mathrm{M^1 L^2 T^{-1} K^{-1}}]$.

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

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

Match List-I with List-II :

List-I (Y vs X) | List-II (Shape of Graph)

(A) Y = magnetic susceptibility, X = magnetising field — (I)

straight line through origin with positive slope

(B) Y = magnetic field, X = distance from centre of a current carrying wire for $x < a$ (where a = radius of wire) — (II)

curve starting flat at high Y then falling off sharply at large X

(C) Y = magnetic field, X = distance from centre of a current carrying wire for $x > a$ (where a = radius of wire) — (III)

horizontal line, Y constant with X

(D) Y = magnetic field inside solenoid, X = distance from centre — (IV)

curve decreasing steeply then levelling off near zero (hyperbola-like decay)

Choose the correct answer from the options given below :

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

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

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

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

In a vernier calliper, when both jaws touch each other, zero of the vernier scale shifts towards left and its $4^{\text{th}}$ 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 mm then how many main scale divisions are there in 1 cm ?

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

Two identical conducting spheres P and S with charge Q on each, repel each other with a force 16 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 :

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

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

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

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

When UV light of wavelength 300 nm is incident on the metal surface having work function 2.13 eV, electron emission takes place. The stopping potential is : (Given $hc = 1240\ \mathrm{eV\,nm}$)

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

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

In finding out refractive index of glass slab the following observations were made through travelling microscope 50 vernier scale division = 49 MSD; 20 divisions on main scale in each cm

For mark on paper

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

For mark on paper seen through slab

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

For powder particle on the top surface of the glass slab

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

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

Refractive index of the glass slab is :

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

A capacitor of 10 μF capacitance whose plates are separated by 10 mm through air and each plate has area $4\ \mathrm{cm^2}$ 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 N. The supply voltage is ________ V.

parallel-plate capacitor of plate separation d, left half filled with dielectric $K_1 = 2$ and right half with $K_2 = 3$, side by side

In the given figure an ammeter A consists of a 240 Ω coil connected in parallel to a 10 Ω shunt. The reading of the ammeter is ________ mA.

series circuit with a 140.4 Ω resistor, a 24 V battery, and the ammeter A

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

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

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

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 $5 \times 10^{-3}\ \mathrm{m^2}$, carrying current of 1 mA is placed in uniform magnetic field of 0.20 T such a way that plane of coil is perpendicular to the magnetic field. The work done in turning the coil through $90°$ is ________ μJ.

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

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

wire of total span 2L fixed between two walls, midpoint sagging by x with angle θ at the supports, 2 kg mass hanging from the midpoint