JEE Main 2024 Jan 30 Shift 1 — Physics

Match List - I with List - II.

	List - I		List - II
(A)	Coefficient of viscosity	(I)	$[\mathrm{M\,L^2\,T^{-2}}]$
(B)	Surface tension	(II)	$[\mathrm{M\,L^2\,T^{-1}}]$
(C)	Angular momentum	(III)	$[\mathrm{M\,L^{-1}\,T^{-1}}]$
(D)	Rotational kinetic energy	(IV)	$[\mathrm{M\,L^0\,T^{-2}}]$

Choose the correct answer from the options given below :

A particle of mass m is projected with a velocity 'u' making an angle of $30°$ with the horizontal. The magnitude of angular momentum of the projectile about the point of projection when the particle is at its maximum height h is :

A spherical body of mass 100 g is dropped from a height of 10 m from the ground. After hitting the ground, the body rebounds to a height of 5 m. The impulse of force imparted by the ground to the body is given by : (given, $\mathrm{g} = 9.8~\mathrm{m/s^2}$)

All surfaces shown in figure are assumed to be frictionless and the pulleys and the string are light. The acceleration of the block of mass 2 kg is :

a 2 kg block on a $30°$ incline connected by a string over pulleys to a hanging 4 kg block; a movable pulley hangs from the ceiling

A particle is placed at the point A of a frictionless track ABC as shown in figure. It is gently pushed towards right. The speed of the particle when it reaches the point B is : (Take $\mathrm{g} = 10~\mathrm{m/s^2}$).

a curved track with point A at height 1 m, point B at height 0.5 m inside a valley, and point C at the top on the right

The gravitational potential at a point above the surface of earth is $-5.12 \times 10^7~\mathrm{J/kg}$ and the acceleration due to gravity at that point is $6.4~\mathrm{m/s^2}$. Assume that the mean radius of earth to be 6400 km. The height of this point above the earth's surface is :

Young's modules of material of a wire of length 'L' and cross-sectional area A is Y. If the length of the wire is doubled and cross-sectional area is halved then Young's modules will be :

Two thermodynamical processes are shown in the figure. The molar heat capacity for process A and B are $\mathrm{C_A}$ and $\mathrm{C_B}$. The molar heat capacity at constant pressure and constant volume are represented by $\mathrm{C_P}$ and $\mathrm{C_V}$, respectively. Choose the correct statement.

log P vs log V graph; process A is a straight line through origin at angle $\tan^{-1}\gamma$, process B is a straight line at $45°$

At which temperature the r.m.s. velocity of a hydrogen molecule equal to that of an oxygen molecule at $47~°\mathrm{C}$ ?

The electrostatic potential due to an electric dipole at a distance 'r' varies as :

An electric toaster has resistance of $60~\Omega$ at room temperature ($27~°\mathrm{C}$). The toaster is connected to a 220 V supply. If the current flowing through it reaches 2.75 A, the temperature attained by toaster is around : ( if $\alpha = 2 \times 10^{-4}/°\mathrm{C}$)

Two insulated circular loop A and B of radius 'a' carrying a current of 'I' in the anti clockwise direction as shown in the figure. The magnitude of the magnetic induction at the centre will be :

two circular loops of equal radius with a common centre O, loop A horizontal and loop B vertical (mutually perpendicular planes), each carrying current I anticlockwise

A series L.R circuit connected with an ac source $\mathrm{E} = (25 \sin 1000\,\mathrm{t})~\mathrm{V}$ has a power factor of $\frac{1}{\sqrt{2}}$. If the source of emf is changed to $\mathrm{E} = (20 \sin 2000\,\mathrm{t})~\mathrm{V}$, the new power factor of the circuit will be :

The electric field of an electromagnetic wave in free space is represented as $\vec{\mathrm{E}} = \mathrm{E}_0 \cos(\omega t - kz)\,\hat{i}$. The corresponding magnetic induction vector will be :

The diffraction pattern of a light of wavelength 400 nm diffracting from a slit of width 0.2 mm is focused on the focal plane of a convex lens of focal length 100 cm. The width of the $1^{\text{st}}$ secondary maxima will be :

The work function of a substance is 3.0 eV. The longest wavelength of light that can cause the emission of photoelectrons from this substance is approximately;

The ratio of the magnitude of the kinetic energy to the potential energy of an electron in the $5^{\text{th}}$ excited state of a hydrogen atom is :

A Zener diode of breakdown voltage 10 V is used as a voltage regulator as shown in the figure. The current through the Zener diode is :

20 V battery in series with a $200~\Omega$ resistor; a Zener diode in parallel with a branch containing a $500~\Omega$ resistor

A potential divider circuit is shown in figure. The output voltage $\mathrm{V}_0$ is :

a 4 V battery across a series chain of a $3.3~\mathrm{k}\Omega$ resistor followed by seven $100~\Omega$ resistors; $\mathrm{V}_0$ is taken across the last six $100~\Omega$ resistors (tap after the first two resistors)

Primary coil of a transformer is connected to 220 V ac. Primary and secondary turns of the transforms are 100 and 10 respectively. Secondary coil of transformer is connected to two series resistances shown in figure. The output voltage $(\mathrm{V}_0)$ is :

220 V ac source on transformer primary; secondary connected to a $15~\mathrm{k}\Omega$ resistor in series with a $7~\mathrm{k}\Omega$ resistor; $\mathrm{V}_0$ taken across the $7~\mathrm{k}\Omega$ resistor

The displacement and the increase in the velocity of a moving particle in the time interval of t to $(t+1)$ s are 125 m and 50 m/s, respectively. The distance travelled by the particle in $(t+2)^{\text{th}}$ s is ________ m.

Consider a Disc of mass 5 kg, radius 2 m, rotating with angular velocity of 10 rad/s about an axis perpendicular to the plane of rotation. An identical disc is kept gently over the rotating disc along the same axis. The energy dissipated so that both the discs continue to rotate together without slipping is ________ J.

a disc of mass 5 kg and radius 2 m rotating at $\omega = 10~\mathrm{rad/s}$ about a vertical axis through its centre

Each of three blocks P, Q and R shown in figure has a mass of 3 kg. Each of the wires A and B has cross-sectional area $0.005~\mathrm{cm^2}$ and Young's modulus $2 \times 10^{11}~\mathrm{N~m^{-2}}$. Neglecting friction, the longitudinal strain on wire B is ________ $\times 10^{-4}$. (Take $\mathrm{g} = 10~\mathrm{m/s^2}$)

blocks P and Q on a horizontal table connected by wire A; wire B runs from Q over a pulley at the table edge down to hanging block R

In a closed organ pipe, the frequency of fundamental note is 30 Hz. A certain amount of water is now poured in the organ pipe so that the fundamental frequency is increased to 110 Hz. If the organ pipe has a cross-sectional area of $2~\mathrm{cm^2}$, the amount of water poured in the organ tube is ________ g. (Take speed of sound in air is 330 m/s)

A capacitor of capacitance C and potential V has energy E. It is connected to another capacitor of capacitance 2 C and potential 2 V. Then the loss of energy is $\frac{x}{3}\,\mathrm{E}$, where $x$ is ________.

Two cells are connected in opposition as shown. Cell $\mathrm{E}_1$ is of 8 V emf and $2~\Omega$ internal resistance; the cell $\mathrm{E}_2$ is of 2 V emf and $4~\Omega$ internal resistance. The terminal potential difference of cell $\mathrm{E}_2$ is ________ V.

a closed loop with cells $\mathrm{E}_1$ and $\mathrm{E}_2$ connected in opposition between points A, B and C

The horizontal component of earth's magnetic field at a place is $3.5 \times 10^{-5}~\mathrm{T}$. A very long straight conductor carrying current of $\sqrt{2}~\mathrm{A}$ in the direction from South east to North West is placed. The force per unit length experienced by the conductor is ________ $\times 10^{-6}~\mathrm{N/m}$.

A ceiling fan having 3 blades of length 80 cm each is rotating with an angular velocity of 1200 rpm. The magnetic field of earth in that region is 0.5 G and angle of dip is $30°$. The emf induced across the blades is $\mathrm{N}\pi \times 10^{-5}~\mathrm{V}$. The value of N is ________.

The distance between object and its two times magnified real image as produced by a convex lens is 45 cm. The focal length of the lens used is ________ cm.

A electron of hydrogen atom on an excited state is having energy $\mathrm{E_n} = -0.85~\mathrm{eV}$. The maximum number of allowed transitions to lower energy level is ________.