JEE Main 2024 Jan 29 Shift 1 — Physics

The resistance $R = \frac{V}{I}$ where $V = (200 \pm 5)$ V and $I = (20 \pm 0.2)$ A, the percentage error in the measurement of R is :

A body starts moving from rest with constant acceleration covers displacement $S_1$ in first $(p - 1)$ seconds and $S_2$ in first $p$ seconds. The displacement $S_1 + S_2$ will be made in time :

If the radius of curvature of the path of two particles of same mass are in the ratio 3:4, then in order to have constant centripetal force, their velocities will be in the ratio of :

A block of mass 100 kg slides over a distance of 10 m on a horizontal surface. If the co-efficient of friction between the surfaces is 0.4, then the work done against friction (in $J$) is :

The potential energy function (in $J$) of a particle in a region of space is given as $U = (2x^2 + 3y^3 + 2z)$. Here $x$, $y$ and $z$ are in meter. The magnitude of $x$-component of force (in $N$) acting on the particle at point $P$ (1, 2, 3) m is :

At what distance above and below the surface of the earth a body will have same weight. (take radius of earth as $R$.)

Given below are two statements:

Statement I : If a capillary tube is immersed first in cold water and then in hot water, the height of capillary rise will be smaller in hot water.

Statement II : If a capillary tube is immersed first in cold water and then in hot water, the height of capillary rise will be smaller in cold water.

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

A thermodynamic system is taken from an original state A to an intermediate state B by a linear process as shown in the figure. It's volume is then reduced to the original value from B to C by an isobaric process. The total work done by the gas from A to B and B to C would be :

P–V diagram; pressure axis in Dyne/cm² marked 8000 (state A) and 4000 (states B, C); volume axis in m³ marked 3 and 7; straight line from A (3, 8000) to B (7, 4000), then isobaric line from B back to C (3, 4000)

Two vessels A and B are of the same size and are at same temperature. A contains 1g of hydrogen and B contains 1g of oxygen. $\mathrm{P_A}$ and $\mathrm{P_B}$ are the pressures of the gases in A and B respectively, then $\frac{P_A}{P_B}$ is :

Two charges of $5Q$ and $-2Q$ are situated at the points $(3a, 0)$ and $(-5a, 0)$ respectively. The electric flux through a sphere of radius '$4a$' having center at origin is :

The electric current through a wire varies with time as $I = I_0 + \beta t$, where $I_0 = 20$ A and $\beta = 3$ A/s. The amount of electric charge crossed through a section of the wire in 20 s is :

A galvanometer having coil resistance $10\,\Omega$ shows a full scale deflection for a current of 3 mA. For it to measure a current of 8 A, the value of the shunt should be:

A capacitor of capacitance 100 $\mu$F is charged to a potential of 12 V and connected to a 6.4 mH inductor to produce oscillations. The maximum current in the circuit would be :

Match List I with List II

	LIST I		LIST II
A.	$\oint \vec{B} \cdot \vec{dl} = \mu_o i_c + \mu_o \varepsilon_o \dfrac{d\phi_E}{dt}$	I.	Gauss' law for electricity
B.	$\oint \vec{E} \cdot \vec{dl} = \dfrac{d\phi_B}{dt}$	II.	Gauss' law for magnetism
C.	$\oint \vec{E} \cdot \vec{dA} = \dfrac{Q}{\varepsilon_o}$	III.	Faraday law
D.	$\oint \vec{B} \cdot \vec{dA} = 0$	IV.	Ampere - Maxwell law

Choose the correct answer from the options given below:

A biconvex lens of refractive index 1.5 has a focal length of 20 cm in air. Its focal length when immersed in a liquid of refractive index 1.6 will be:

The de-Broglie wavelength of an electron is the same as that of a photon. If velocity of electron is 25% of the velocity of light, then the ratio of K.E. of electron and K.E. of photon will be:

The explosive in a Hydrogen bomb is a mixture of $_1\mathrm{H}^2$, $_1\mathrm{H}^3$ and $_3\mathrm{Li}^6$ in some condensed form. The chain reaction is given by

$$_3\mathrm{Li}^6 + {_0\mathrm{n}^1} \rightarrow {_2\mathrm{He}^4} + {_1\mathrm{H}^3}$$

$$_1\mathrm{H}^2 + {_1\mathrm{H}^3} \rightarrow {_2\mathrm{He}^4} + {_0\mathrm{n}^1}$$

During the explosion the energy released is approximately

[Given ; M (Li) = 6.01690 amu, M ($_1\mathrm{H}^2$) = 2.01471 amu, M ($_2\mathrm{He}^4$) = 4.00388 amu, and 1 amu = 931.5 MeV]

In the given circuit, the breakdown voltage of the Zener diode is 3.0 V. What is the value of $\mathrm{I_z}$?

circuit with a 10 V battery in series with a 1 kΩ resistor; a Zener diode (carrying current $I_z$) connected between nodes A and B in parallel with a 2 kΩ resistor connected between nodes C and D across the output terminals

A convex mirror of radius of curvature 30 cm forms an image that is half the size of the object. The object distance is :

The deflection in moving coil galvanometer falls from 25 divisions to 5 division when a shunt of $24\,\Omega$ is applied. The resistance of galvanometer coil will be :

A ball rolls off the top of a stairway with horizontal velocity $u$. The steps are 0.1 m high and 0.1 m wide. The minimum velocity $u$ with which that ball just hits the step 5 of the stairway will be $\sqrt{x}\ \mathrm{ms}^{-1}$ where $x =$ __________ [use $\mathrm{g} = 10\ \mathrm{m/s^2}$].

A cylinder is rolling down on an inclined plane of inclination $60^\circ$. It's acceleration during rolling down will be $\frac{x}{\sqrt{3}}\ \mathrm{m/s^2}$, where $x =$ ________ (use $\mathrm{g} = 10\ \mathrm{m/s^2}$).

In a test experiment on a model aeroplane in wind tunnel, the flow speeds on the upper and lower surfaces of the wings are $70\ \mathrm{ms}^{-1}$ and $65\ \mathrm{ms}^{-1}$ respectively. If the wing area is $2\ \mathrm{m^2}$, the lift of the wing is _____ $N$.

(Given density of air $= 1.2\ \mathrm{kg\ m^{-3}}$)

When the displacement of a simple harmonic oscillator is one third of its amplitude, the ratio of total energy to the kinetic energy is $\frac{x}{8}$, where $x =$ ________.

An electron is moving under the influence of the electric field of a uniformly charged infinite plane sheet S having surface charge density $+\sigma$. The electron at $t=0$ is at a distance of 1 m from S and has a speed of 1 m/s. The maximum value of $\sigma$ if the electron strikes S at $t=1$ s is $\alpha\left[\frac{m \epsilon_0}{e}\right] \frac{\mathrm{C}}{\mathrm{m}^2}$, the value of $\alpha$ is ______.

A $16\,\Omega$ wire is bend to form a square loop. A 9V battery with internal resistance $1\,\Omega$ is connected across one of its sides. If a $4\,\mu F$ capacitor is connected across one of its diagonals, the energy stored by the capacitor will be $\frac{x}{2}\ \mu J$, where $x =$ __________.

The magnetic potential due to a magnetic dipole at a point on its axis situated at a distance of 20 cm from its center is $1.5 \times 10^{-5}\ T\,m$. The magnetic moment of the dipole is ________ $A\,m^2$. (Given : $\frac{\mu_o}{4\pi} = 10^{-7}\ T\,m\,A^{-1}$)

A square loop of side 10 cm and resistance $0.7\,\Omega$ is placed vertically in east-west plane. A uniform magnetic field of 0.20 $T$ is set up across the plane in north east direction. The magnetic field is decreased to zero in 1 s at a steady rate. Then, magnitude of induced emf is $\sqrt{x} \times 10^{-3}\,V$. The value of $x$ is __________.

In a double slit experiment shown in figure, when light of wavelength 400 nm is used, dark fringe is observed at $P$. If $D=0.2$ m, the minimum distance between the slits $S_1$ and $S_2$ is _______ mm.

source on the left, slits $S_1$ and $S_2$ separated by distance $d$ on a vertical line; source is at distance $D$ from the slit plane and point $P$ is at distance $D$ on the other side, both on the line through $S_2$; dashed lines from source to $S_1$ and from $S_1$ to $P$ form a triangle

When a hydrogen atom going from $n=2$ to $n=1$ emits a photon, its recoil speed is $\frac{x}{5}\ m/s$. Where $x =$ ________. (Use, mass of hydrogen atom $= 1.6 \times 10^{-27}$ kg)