JEE Main 2024 Jan 30 Shift 2 — Physics

If mass is written as $m = k\, c^{P}\, G^{-1/2}\, h^{1/2}$ then the value of $P$ will be : (Constants have their usual meaning with $k$ a dimensionless constant)

Projectiles A and B are thrown at angles of $45°$ and $60°$ with vertical respectively from top of a $400$ m high tower. If their ranges and times of flight are same, the ratio of their speeds of projection $v_{\mathrm{A}} : v_{\mathrm{B}}$ is :

[Take $g = 10\ ms^{-2}$]

Three blocks $A$, $B$ and $C$ are pulled on a horizontal smooth surface by a force of $80N$ as shown in figure

blocks A (5 kg), B (3 kg) and C (2 kg) in a row connected by strings with tensions $T_1$ (between A and B) and $T_2$ (between B and C); force $F = 80N$ applied to C towards the right

The tensions $T_1$ and $T_2$ in the string are respectively:

A block of mass $m$ is placed on a surface having vertical crossection given by $y = x^2/4$. If coefficient of friction is $0.5$, the maximum height above the ground at which block can be placed without slipping is:

A block of mass $1$ kg is pushed up a surface inclined to horizontal at an angle of $60°$ by a force of $10\ N$ parallel to the inclined surface as shown in figure. When the block is pushed up by $10\ m$ along inclined surface, the work done against frictional force is :

[$g = 10\ m/s^2$]

incline at $60°$ to the horizontal with block $M$ on it, coefficient of static friction $\mu_s = 0.1$, force of $10\ N$ applied up along the incline

Escape velocity of a body from earth is $11.2\ km/s$. If the radius of a planet be one-third the radius of earth and mass be one-sixth that of earth, the escape velocity from the planet is :

A block of ice at $-10°C$ is slowly heated and converted to steam at $100°C$. Which of the following curves represent the phenomenon qualitatively:

Choose the correct statement for processes $A$ & $B$ shown in figure.

P–V diagram with two downward-sloping curves; curve A is lower and less steep, curve B is higher and steeper, both with arrows directed toward increasing V

If three moles of monoatomic gas $\left(\gamma = \frac{5}{3}\right)$ is mixed with two moles of a diatomic gas $\left(\gamma = \frac{7}{5}\right)$, the value of adiabatic exponent $\gamma$ for the mixture is

A particle of charge '$-q$' and mass '$m$' moves in a circle of radius '$r$' around an infinitely long line charge of linear charge density '$+\lambda$'. Then time period will be given as :

(Consider $k$ as Coulomb's constant)

When a potential difference $V$ is applied across a wire of resistance $R$, it dissipates energy at a rate $W$. If the wire is cut into two halves and these halves are connected mutually parallel across the same supply, the energy dissipation rate will become:

Match List I with List II

	List I		List II
A.	Gauss's law of magnetostatics	I.	$\oint \vec{E} \cdot \vec{da} = \dfrac{1}{\varepsilon_o} \int \rho \, dV$
B.	Faraday's law of electro magnetic induction	II.	$\oint \vec{B} \cdot \vec{da} = 0$
C.	Ampere's law	III.	$\int \vec{E} \cdot \vec{dl} = \dfrac{-d}{dt} \int \vec{B} \cdot \vec{da}$
D.	Gauss's law of electrostatics	IV.	$\oint \vec{B} \cdot \vec{dl} = \mu_0 I$

Choose the correct answer from the options given below:

An alternating voltage $V(t) = 220 \sin 100\pi t$ volt is applied to a purely resistive load of $50\ \Omega$. The time taken for the current to rise from half of the peak value to the peak value is:

If the total energy transferred to a surface in time $t$ is $6.48 \times 10^5\ J$, then the magnitude of the total momentum delivered to this surface for complete absorption will be:

A beam of unpolarised light of intensity $I_o$ is passed through a polaroid $A$ and then through another polaroid $B$ which is oriented so that its principal plane makes an angle of $45°$ relative to that of $A$. The intensity of emergent light is:

For the photoelectric effect, the maximum kinetic energy $(E_k)$ of the photoelectrons is plotted against the frequency $(\nu)$ of the incident photons as shown in figure. The slope of the graph gives

straight-line graph of $E_k$ (y-axis) versus $\nu$ (x-axis), intersecting the $\nu$-axis at a positive intercept and making angle $\theta$ with it

In a nuclear fission reaction of an isotope of mass $M$, three similar daughter nuclei of same mass are formed. The speed of a daughter nuclei in terms of mass defect $\Delta M$ will be :

An electron revolving in $n^{\text{th}}$ Bohr orbit has magnetic moment $\mu_n$. If $\mu_n \propto n^x$, the value of $x$ is

series circuit with a 15 V battery, diode $D_1$ (Ge) and diode $D_2$ (Si) both forward biased, a $1.5\ k\Omega$ resistor, and a load resistance $R_L = 2.5\ k\Omega$ across which the voltage is measured

In the given circuit, the voltage across load resistance $(R_L)$ is:

If $50$ Vernier divisions are equal to $49$ main scale divisions of a traveling microscope and one smallest reading of main scale is $0.5\ mm$, the Vernier constant of traveling microscope is

A vector has magnitude same as that of $\vec{A} = 3\hat{i} + 4\hat{j}$ and is parallel to $\vec{B} = 4\hat{i} + 3\hat{j}$. The $x$ and $y$ components of this vector in first quadrant are $x$ and $3$ respectively where $x =$ ________.

Two discs of moment of inertia $I_1 = 4\ kg\ m^2$ and $I_2 = 2\ kg\ m^2$, about their central axes & normal to their planes, rotating with angular speeds $10\ rad/s$ & $4\ rad/s$ respectively are brought into contact face to face with their axes of rotation coincident. The loss in kinetic energy of the system in the process is ________ J.

A big drop is formed by coalescing $1000$ small identical drops of water. If $E_1$ be the total surface energy of $1000$ small drops of water and $E_2$ be the surface energy of single big drop of water, then $E_1 : E_2$ is $x : 1$ where $x =$ _______.

A point source is emitting sound waves of intensity $16 \times 10^{-8}\ Wm^{-2}$ at the origin. The difference in intensity (magnitude only) at two points located at a distances of $2m$ and $4m$ from the origin respectively will be _______ $\times\ 10^{-8}\ Wm^{-2}$.

Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of $37°$ with each other. When suspended in a liquid of density $0.7\ g/cm^3$, the angle remains same. If density of material of the sphere is $1.4\ g/cm^3$, the dielectric constant of the liquid is _______ $\left(\tan 37° = \frac{3}{4}\right)$

Two resistance of $100\ \Omega$ and $200\ \Omega$ are connected in series with a battery of $4\ V$ and negligible internal resistance . A voltmeter is used to measure voltage across $100\ \Omega$ resistance, which gives reading as $1\ V$. The resistance of voltmeter must be _______ $\Omega$.

The current of $5A$ flows in a square loop of sides $1\ m$ is placed in air. The magnetic field at the centre of the loop is $X\sqrt{2} \times 10^{-7}\ T$. The value of $X$ is ________.

A power transmission line feeds input power at $2.3\ kV$ to a step down transformer with its primary winding having $3000$ turns. The output power is delivered at $230\ V$ by the transformer. The current in the primary of the transformer is $5A$ and its efficiency is $90\%$. The winding of transformer is made of copper. The output current of transformer is _______ $A$.

In an experiment to measure the focal length $(f)$ of a convex lens, the magnitude of object distance $(x)$ and the image distance $(y)$ are measured with reference to the focal point of the lens. The $y$-$x$ plot is shown in figure.

The focal length of the lens is ________ $cm$.

y–x graph with y (cm) and x (cm) axes marked 10 to 40; data points A, B, C, D, E lie on a downward-sloping curve/line, with point C near (20, 20)

A simple pendulum is placed at a place where its distance from the earth's surface is equal to the radius of the earth. If the length of the string is $4m$, then the time period of small oscillations will be _______ $s$. [take $g = \pi^2\ ms^{-2}$]