JEE Main 2024 Apr 6 Shift 1 — Physics

Four particles $A, B, C, D$ of mass $\frac{m}{2}, m, 2m, 4m$, have same momentum, respectively. The particle with maximum kinetic energy is :

A light string passing over a smooth light pulley connects two blocks of masses $m_1$ and $m_2$ (where $m_2 > m_1$). If the acceleration of the system is $\frac{g}{\sqrt{2}}$, then the ratio of the masses $\frac{m_1}{m_2}$ is:

To project a body of mass m from earth's surface to infinity, the required kinetic energy is (assume, the radius of earth is $R_E$, $g$ = acceleration due to gravity on the surface of earth):

A train starting from rest first accelerates uniformly up to a speed of 80 $km/h$ for time $t$, then it moves with a constant speed for time $3t$. The average speed of the train for this duration of journey will be (in $km/h$) :

A small ball of mass m and density $\rho$ is dropped in a viscous liquid of density $\rho_0$. After sometime, the ball falls with constant velocity. The viscous force on the ball is :

The specific heat at constant pressure of a real gas obeying $PV^2 = RT$ equation is:

A sample contains mixture of helium and oxygen gas. The ratio of root mean square speed of helium and oxygen in the sample, is :

$\sigma$ is the uniform surface charge density of a thin spherical shell of radius $R$. The electric field at any point on the surface of the spherical shell is :

Electromagnetic waves travel in a medium with speed of $1.5\times10^{8}\ \mathrm{m\ s^{-1}}$. The relative permeability of the medium is 2.0. The relative permittivity will be:

The value of unknown resistance $(x)$ for which the potential difference between $B$ and $D$ will be zero in the arrangement shown, is :

Wheatstone-bridge-like network between A and C. Upper-left arm A to B: $24\,\Omega$ in parallel with series $12\,\Omega$ and $12\,\Omega$; upper-right arm B to C: $1\,\Omega$ in parallel with $1\,\Omega$; lower-left arm A to D: $x\,\Omega$ in parallel with series $12\,\Omega$ and $12\,\Omega$; lower-right arm D to C: $0.5\,\Omega$; battery of $14.5\,V$ connected across A and C

While measuring diameter of wire using screw gauge the following readings were noted. Main scale reading is 1 mm and circular scale reading is equal to 42 divisions. Pitch of screw gauge is 1 mm and it has 100 divisions on circular scale. The diameter of the wire is $\frac{x}{50}\ mm$. The value of $x$ is :

Match List I with List II

	LIST I		LIST II
A.	Torque	I.	$[M^1L^1T^{-2}A^{-2}]$
B.	Magnetic field	II.	$[L^2A^1]$
C.	Magnetic moment	III.	$[M^1T^{-2}A^{-1}]$
D.	Permeability of free space	IV.	$[M^1L^2T^{-2}]$

Choose the correct answer from the options given below:

An element $\Delta l = \Delta x\,\hat{i}$ is placed at the origin and carries a large current $I = 10\mathrm{A}$. The magnetic field on the $y$-axis at a distance of 0.5m from the elements $\Delta x$ of 1cm length is :

current element $\Delta x$ along the x-axis at the origin; point $P$ on the y-axis at a distance $0.5\,m$ above the element

Given below are two statements :

Statement I : In an LCR series circuit, current is maximum at resonance.

Statement II : Current in a purely resistive circuit can never be less than that in a series LCR circuit when connected to same voltage source.

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

To find the spring constant $(k)$ of a spring experimentally, a student commits 2% positive error in the measurement of time and 1% negative error in measurement of mass. The percentage error in determining value of $k$ is :

Which of the following phenomena does not explain by wave nature of light.

A. reflection B. diffraction C. photoelectric effect D. interference E. polarization

Choose the most appropriate answer from the options given below:

In photoelectric experiment energy of 2.48 eV irradiates a photo sensitive material. The stopping potential was measured to be 0.5 V. Work function of the photo sensitive material is :

The ratio of the shortest wavelength of Balmer series to the shortest wavelength of Lyman series for hydrogen atom is :

The correct truth table for the following logic circuit is :

logic circuit — inputs A and B feed an AND gate; input A also passes through a NOT gate; the NOT-gate output and the AND-gate output feed an OR gate whose output is Y

A bullet of mass $50g$ is fired with a speed 100 m/s on a plywood and emerges with 40 m/s. The percentage loss of kinetic energy is :

The refractive index of prism is $\mu = \sqrt{3}$ and the ratio of the angle of minimum deviation to the angle of prism is one. The value of angle of prism is _________ $^\circ$.

A particle is doing simple harmonic motion of amplitude 0.06 m and time period 3.14 s. The maximum velocity of the particle is _________ cm/s.

For three vectors $\vec{A} = (-x\hat{i} - 6\hat{j} - 2\hat{k})$, $\vec{B} = (-\hat{i} + 4\hat{j} + 3\hat{k})$ and $\vec{C} = (-8\hat{i} - \hat{j} + 3\hat{k})$, if $\vec{A}\cdot(\vec{B}\times\vec{C}) = 0$, then value of $x$ is _________.

A big drop is formed by coalescing 1000 small droplets of water. The ratio of surface energy of 1000 droplets to that of energy of big drop is $\frac{10}{x}$. The value of $x$ is _________.

When a $dc$ voltage of 100V is applied to an inductor, a $dc$ current of 5A flows through it. When an $ac$ voltage of 200V peak value is connected to inductor, its inductive reactance is found to be $20\sqrt{3}\,\Omega$. The power dissipated in the circuit is _________ $W$.

If the radius of earth is reduced to three-fourth of its present value without change in its mass then value of duration of the day of earth will be _________ hours 30 minutes.

A circular coil having 200 turns, $2.5\times10^{-4}\ \mathrm{m^2}$ area and carrying $100\ \mu A$ current is placed in a uniform magnetic field of 1T. Initially the magnetic dipole moment $(\vec{M})$ was directed along $\vec{B}$. Amount of work, required to rotate the coil through $90^\circ$ from its initial orientation such that $\vec{M}$ becomes perpendicular to $\vec{B}$, is _________ $\mu J$.

A wire of resistance $R$ and radius $r$ is stretched till its radius became $r/2$. If new resistance of the stretched wire is $x\,R$, then value of $x$ is _________.

Three infinitely long charged thin sheets are placed as shown in figure. The magnitude of electric field at the point $P$ is $\frac{x\sigma}{\epsilon_o}$. The value of $x$ is _________ (all quantities are measured in SI units).

three vertical sheets parallel to the YZ plane — sheet with charge density $-\sigma$ at $X=-a$, sheet with $-2\sigma$ at $X=a$, sheet with $\sigma$ at $X=3a$; point $P$ lies between $X=a$ and $X=3a$

Radius of a certain orbit of hydrogen atom is 8.48 Å. If energy of electron in this orbit is $E/x$, then $x =$ _________.

(Given $\mathrm{a}_o = 0.529$ Å, $E$ = energy of electron in ground state).