JEE Main 2024 Apr 5 Shift 1 — Physics

If G be the gravitational constant and u be the energy density then which of the following quantity have the dimensions as that of the $\sqrt{uG}$ :

The angle between vector $\vec{Q}$ and the resultant of $\left(2\vec{Q} + 2\vec{P}\right)$ and $\left(2\vec{Q} - 2\vec{P}\right)$ is :

A wooden block of mass 5 kg rests on a soft horizontal floor. When an iron cylinder of mass 25 kg is placed on the top of the block, the floor yields and the block and the cylinder together go down with an acceleration of $0.1\ \mathrm{ms}^{-2}$. The action force of the system on the floor is equal to :

A body of mass 50 kg is lifted to a height of 20 m from the ground in the two different ways as shown in the figures. The ratio of work done against the gravity in both the respective cases, will be :

Case-1 — block of M = 50 kg pulled straight up a height h = 20 m; Case-2 — the same mass moved along a ramp inclined at 30° to the same height h = 20 m

Ratio of radius of gyration of a hollow sphere to that of a solid cylinder of equal mass, for moment of Inertia about their diameter axis AB as shown in figure is $\sqrt{\frac{8}{x}}$. The value of $x$ is :

a hollow sphere of mass M and radius R with diameter axis AB, and a solid cylinder of diameter 2R and length 4R with axis AB through its centre perpendicular to its length

Match List I with List II :

List I	List II
(A) Kinetic energy of planet	(I) $-\frac{GMm}{a}$
(B) Gravitation Potential energy of sun-planet system	(II) $\frac{GMm}{2a}$
(C) Total mechanical energy of planet	(III) $\frac{Gm}{r}$
(D) Escape energy at the surface of planet for unit mass object	(IV) $-\frac{GMm}{2a}$

(Where a = radius of planet orbit, r = radius of planet, M = mass of Sun, m = mass of planet)

Choose the correct answer from the options given below :

Given below are two statements :

Statement I : When a capillary tube is dipped into a liquid, the liquid neither rises nor falls in the capillary. The contact angle may be 0°.

Statement II : The contact angle between a solid and a liquid is a property of the material of the solid and liquid as well.

In the light of the above statement, choose the correct answer from the options given below.

The heat absorbed by a system in going through the given cyclic process is :

a circular cyclic process on a P–V diagram; vertical axis labelled P (in cc) with dashed lines at 60 and 340, horizontal axis labelled V (in kPa) with dashed lines at 60 and 340, the circle traversed clockwise

If the collision frequency of hydrogen molecules in a closed chamber at 27°C is Z, then the collision frequency of the same system at 127°C is :

A simple pendulum doing small oscillations at a place R height above earth surface has time period of $T_1 = 4$ s. $T_2$ would be it's time period if it is brought to a point which is at a height 2R from earth surface. Choose the correct relation [R = radius of earth] :

In hydrogen like system the ratio of coulombian force and gravitational force between an electron and a proton is in the order of :

In the given figure $R_1 = 10\,\Omega$, $R_2 = 8\,\Omega$, $R_3 = 4\,\Omega$ and $R_4 = 8\,\Omega$. Battery is ideal with emf 12V. Equivalent resistant of the circuit and current supplied by battery are respectively :

circuit with a 12 V battery; $R_1$ in the top branch, and $R_2$, $R_4$ and $R_3$ connected in parallel between the two nodes

In a co-axial straight cable, the central conductor and the outer conductor carry equal currents in opposite directions. The magnetic field is zero :

Two conducting circular loops A and B are placed in the same plane with their centres coinciding as shown in figure. The mutual inductance between them is :

two concentric coplanar circular loops — small inner loop A of radius a and large outer loop B of radius b, with b >> a

An alternating voltage of amplitude 40 V and frequency 4 kHz is applied directly across the capacitor of $12\ \mu\mathrm{F}$. The maximum displacement current between the plates of the capacitor is nearly :

Light emerges out of a convex lens when a source of light kept at its focus. The shape of wavefront of the light is :

Given below are two statements :

graph of stopping potential $V_0$ versus frequency $\nu$ showing two parallel straight lines for materials $M_1$ and $M_2$, with the line for $M_1$ to the left of $M_2$

Statement I : Figure shows the variation of stopping potential with frequency ($\nu$) for the two photosensitive materials $M_1$ and $M_2$. The slope gives value of $\frac{h}{e}$, where h is Planck's constant, e is the charge of electron.

Statement II : $M_2$ will emit photoelectrons of greater kinetic energy for the incident radiation having same frequency.

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

An electron rotates in a circle around a nucleus having positive charge Ze. Correct relation between total energy (E) of electron to its potential energy (U) is :

Following gates section is connected in a complete suitable circuit.

logic circuit — input A through a NOT/NOR gate, inputs B and C through a NAND gate, both outputs feeding a NOR gate; input D through an OR gate; the NOR gate output and the OR gate output connect through a resistance R to a DC bulb

For which of the following combination, bulb will glow (ON) :

Time periods of oscillation of the same simple pendulum measured using four different measuring clocks were recorded as 4.62 s, 4.632 s, 4.6 s and 4.64 s. The arithmetic mean of these readings in correct significant figure is :

A body moves on a frictionless plane starting from rest. If $S_n$ is distance moved between $t = n-1$ and $t = n$ and $S_{n-1}$ is distance moved between $t = n-2$ and $t = n-1$, then the ratio $\frac{S_{n-1}}{S_n}$ is $\left(1 - \frac{2}{x}\right)$ for $n = 10$. The value of $x$ is ________.

Three blocks $M_1$, $M_2$, $M_3$ having masses 4 kg, 6 kg and 10 kg respectively are hanging from a smooth pully using rope 1, 2 and 3 as shown in figure. The tension in the rope 1, $T_1$ when they are moving upward with acceleration of $2\,\mathrm{ms}^{-2}$ is ________ N(if $g = 10\ \mathrm{m/s^2}$).

three blocks $M_1$ (4 kg), $M_2$ (6 kg), $M_3$ (10 kg) hanging vertically one below the other from a pulley, connected by ropes 1, 2 and 3 with tensions $T_1$, $T_2$, $T_3$, the whole system accelerating at 2 m/s²

The density and breaking stress of a wire are $6 \times 10^4\ \mathrm{kg/m^3}$ and $1.2 \times 10^8\ \mathrm{N/m^2}$ respectively. The wire is suspended from a rigid support on a planet where acceleration due to gravity is $\frac{1}{3}^{\text{rd}}$ of the value on the surface of earth. The maximum length of the wire with breaking is ________ m (take, $g = 10\ \mathrm{m/s^2}$).

Three capacitors of capacitances $25\ \mu\mathrm{F}$, $30\ \mu\mathrm{F}$ and $45\ \mu\mathrm{F}$ are connected in parallel to a supply of 100 V. Energy stored in the above combination is E. When these capacitors are connected in series to the same supply, the stored energy is $\frac{9}{x}$ E. The value of $x$ is ________.

The electric field between the two parallel plates of a capacitor of $1.5\ \mu\mathrm{F}$ capacitance drops to one third of its initial value in $6.6\ \mu\mathrm{s}$ when the plates are connected by a thin wire. The resistance of this wire is ________ $\Omega$. (Given, $\log 3 = 1.1$)

A 2A current carrying straight metal wire of resistance $1\ \Omega$, resistivity $2 \times 10^{-6}\ \Omega\mathrm{m}$, area of cross-section $10\ \mathrm{mm}^2$ and mass 500 g is suspended horizontally in mid air by applying a uniform magnetic field $\vec{B}$. The magnitude of B is ________ $\times 10^{-1}$ T (given, $g = 10\ \mathrm{m/s^2}$).

An ac source is connected in given series LCR circuit. The rms potential difference across the capacitor of $20\ \mu\mathrm{F}$ is ________ V.

series LCR circuit with L = 1H, C = 20 μF, R = 300 Ω connected to an ac source $V = 50\sqrt{2} \sin 100t$ volt

In Young's double slit experiment, carried out with light of wavelength 5000 Å, the distance between the slits is 0.3 mm and the screen is at 200 cm from the slits. The central maximum is at $x = 0$ cm. The value of $x$ for third maxima is ________ mm.

If three helium nuclei combine to form a carbon nucleus then the energy released in this reaction is ________ $\times 10^{-2}$ MeV. (Given $1\ \mathrm{u} = 931\ \mathrm{MeV/c^2}$, atomic mass of helium $= 4.002603\mathrm{u}$)

In the experiment to determine the galvanometer resistance by half-deflection method, the plot of $\frac{1}{\theta}$ vs the resistance (R) of the resistance box is shown in the figure. The figure of merit of the galvanometer is ________ $\times 10^{-1}$ A/division. [The source has emf 2V]

straight-line graph of $\frac{1}{\theta}\ (\mathrm{div}^{-1})$ on the y-axis (markings at ½, 1, 1½, 2) versus $R\ (\Omega)$ on the x-axis (markings at 2, 4, 6); dashed lines indicate points near (2, 1), (4, 1½) and (6, 2)