JEE Main 2024 Apr 9 Shift 2 — Physics

The de-Broglie wavelength associated with a particle of mass $m$ and energy $E$ is $h/\sqrt{2mE}$. The dimensional formula for Planck's constant is :

Two cars are travelling towards each other at speed of $20~\mathrm{m~s^{-1}}$ each. When the cars are 300 m apart, both the drivers apply brakes and the cars retard at the rate of $2~\mathrm{m~s^{-2}}$. The distance between them when they come to rest is :

A nucleus at rest disintegrates into two smaller nuclei with their masses in the ratio of 2:1. After disintegration they will move :

A 1 kg mass is suspended from the ceiling by a rope of length 4m. A horizontal force '$F$' is applied at the mid point of the rope so that the rope makes an angle of $45°$ with respect to the vertical axis as shown in figure. The magnitude of $F$ is :

(Assume that the system is in equilibrium and $g = 10~\mathrm{m/s^2}$)

a rope hangs from the ceiling; at its midpoint a horizontal force $\vec{F}$ acts to the left, the upper segment $T_1$ makes $\theta = 45°$ with the vertical, and the lower segment $T_2$ carries a 1 kg block

A hydrogen atom in ground state is given an energy of 10.2 eV. How many spectral lines will be emitted due to transition of electrons ?

A real gas within a closed chamber at $27°C$ undergoes the cyclic process as shown in figure. The gas obeys $PV^3 = RT$ equation for the path $A$ to $B$. The net work done in the complete cycle is (assuming $R = 8$ J/mol K) :

P–V diagram with $P$ in $\mathrm{N/m^2}$ and $V$ in $\mathrm{m^3}$; curve from A (2, 20) to B (4, 10), horizontal line from B back to C (2, 10), and vertical line from C up to A

The energy released in the fusion of 2 kg of hydrogen deep in the sun is $E_H$ and the energy released in the fission of 2 kg of $^{235}\mathrm{U}$ is $E_U$. The ratio $\frac{E_H}{E_U}$ is approximately:

(Consider the fusion reaction as $4{}^{1}_{1}\mathrm{H} + 2e^- \rightarrow {}^{4}_{2}He + 2\nu + 6\gamma + 26.7$ MeV, energy released in the fission reaction of $^{235}\mathrm{U}$ is 200 $MeV$ per fission nucleus and $\mathrm{N_A} = 6.023\times10^{23}$)

A satellite of $10^3$ kg mass is revolving in circular orbit of radius $2R$. If $\frac{10^4 R}{6}$ J energy is supplied to the satellite, it would revolve in a new circular orbit of radius :

(use $g = 10~\mathrm{m/s^2}$, $R$ = radius of earth)

The excess pressure inside a soap bubble is thrice the excess pressure inside a second soap bubble. The ratio between the volume of the first and the second bubble is:

A spherical ball of radius $1\times10^{-4}$ m and density $10^5~\mathrm{kg/m^3}$ falls freely under gravity through a distance $h$ before entering a tank of water. If after entering in water the velocity of the ball does not change, then the value of $h$ is approximately:

(The coefficient of viscosity of water is $9.8\times10^{-6}~N~s/m^2$)

The temperature of a gas is $-78°\mathrm{C}$ and the average translational kinetic energy of its molecules is K. The temperature at which the average translational kinetic energy of the molecules of the same gas becomes 2K is :

Five charges $+q$, $+5q$, $-2q$, $+3q$ and $-4q$ are situated as shown in the figure. The electric flux due to this configuration through the surface $S$ is :

an irregular closed surface S enclosing charges $+5q$, $q$ and $-2q$; charges $+3q$ and $-4q$ lie outside the surface

The effective resistance between $A$ and $B$, if resistance of each resistor is $R$, will be :

resistor network — from A a resistor R leads to a diamond of resistors (two R in the upper arms, two R in the lower arms) with two vertical bridge resistors R and two horizontal middle resistors R meeting at the centre, then a resistor R leads to B

A proton and a deutron ($q = +e$, $m = 2.0\mathrm{u}$) having same kinetic energies enter a region of uniform magnetic field $\vec{B}$, moving perpendicular to $\vec{B}$. The ratio of the radius $r_d$ of deutron path to the radius $r_p$ of the proton path is :

A square loop of side 15 cm being moved towards right at a constant speed of 2 cm/s as shown in figure. The front edge enters the 50 cm wide magnetic field at $t = 0$. The value of induced emf in the loop at $t = 10$ s will be :

a 15 cm square loop moving right at 2 cm/s towards a 50 cm wide region of uniform magnetic field $B = 1.0~\mathrm{T}$ directed into the page

The following figure represents two biconvex lenses $L_1$ and $L_2$ having focal length 10 cm and 15 cm respectively. The distance between $L_1$ & $L_2$ is :

parallel rays enter biconvex lens $L_1$, converge and then pass through biconvex lens $L_2$, emerging parallel to the axis

UV light of 4.13 eV is incident on a photosensitive metal surface having work function 3.13 eV. The maximum kinetic energy of ejected photoelectrons will be:

logic circuit — inputs A and B feed an AND gate whose output goes to one input of a NOR gate giving output E; A and B also each pass through NOT gates into a second AND gate whose output goes to the other input of the NOR gate

Truth table:

A	B	E
0	0	0
0	1	X
1	0	Y
1	1	0

In the truth table of the above circuit the value of X and Y are :

The $I$-$V$ characteristics of an electronic device shown in the figure. The device is :

I–V curve — small current for positive V rising near the origin, and for negative V a nearly constant small reverse current of $5(\mu A)$ that drops sharply at a large negative (breakdown) voltage

The magnetic field in a plane electromagnetic wave is $\mathrm{B_y} = (3.5\times10^{-7})\sin(1.5\times10^3 x + 0.5\times10^{11} t)$ T. The corresponding electric field will be :

A force $(3x^2 + 2x - 5)$ N displaces a body from $x = 2$ m to $x = 4$ m. Work done by this force is ________ $J$.

Monochromatic light of wavelength 500 nm is used in Young's double slit experiment. An interference pattern is obtained on a screen. When one of the slits is covered with a very thin glass plate (refractive index = 1.5), the central maximum is shifted to a position previously occupied by the $4^{th}$ bright fringe. The thickness of the glass-plate is ________ $\mu$m.

A capacitor of reactance $4\sqrt{3}~\Omega$ and a resistor of resistance $4~\Omega$ are connected in series with an ac source of peak value $8\sqrt{2}$ V. The power dissipation in the circuit is ________ W.

A straight magnetic strip has a magnetic moment of 44 $\mathrm{Am^2}$. If the strip is bent in a semicircular shape, its magnetic moment will be ________ $\mathrm{Am^2}$.

(given $\pi = \frac{22}{7}$)

At room temperature ($27°C$), the resistance of a heating element is $50~\Omega$. The temperature coefficient of the material is $2.4\times10^{-4}~°C^{-1}$. The temperature of the element, when its resistance is $62~\Omega$, is ________ $°C$.

An electric field $\vec{E} = (2x\hat{i})\,\mathrm{NC^{-1}}$ exists in space. A cube of side 2m is placed in the space as per figure given below. The electric flux through the cube is ________ $\mathrm{Nm^2/C}$.

a cube of side 2 m placed with one face in the y–z plane at a distance 2 m from the origin along the x-axis

A particle of mass 0.50 $kg$ executes simple harmonic motion under force $F = -50~(\mathrm{Nm^{-1}})\,x$. The time period of oscillation is $\frac{x}{35}$ s. The value of $x$ is ________ .

(Given $\pi = \frac{22}{7}$)

A circular disc reaches from top to bottom of an inclined plane of length $l$. When it slips down the plane, it takes $t$ s. When it rolls down the plane then it takes $\left(\frac{\alpha}{2}\right)^{1/2} t$ s, where $\alpha$ is ________ .

The resultant of two vectors $\vec{A}$ and $\vec{B}$ is perpendicular to $\vec{A}$ and its magnitude is half that of $\vec{B}$. The angle between vectors $\vec{A}$ and $\vec{B}$ is ________ $°$.

To determine the resistance ($R$) of a wire, a circuit is designed below. The $V$-$I$ characteristic curve for this circuit is plotted for the voltmeter and the ammeter readings as shown in figure. The value of $R$ is __________ $\Omega$.

circuit — a voltmeter V of internal resistance 10 kΩ connected in parallel with resistance R, in series with a milliammeter (mA) and a variable source E; below it a graph of $I$(mA) versus $V$(volt) showing a straight line through the origin passing through points (4, 2), (6, 3) and (8, 4)