JEE Main 2024 Apr 5 Shift 2 — Physics

What is the dimensional formula of $ab^{-1}$ in the equation $\left(P + \frac{a}{V^2}\right)(V - b) = RT$, where letters have their usual meaning.

A man carrying a monkey on his shoulder does cycling smoothly on a circular track of radius $9\ \mathrm{m}$ and completes 120 resolutions in 3 minutes. The magnitude of centripetal acceleration of monkey is (in $\mathrm{m/s^2}$) :

A heavy box of mass 50 kg is moving on a horizontal surface. If co-efficient of kinetic friction between the box and horizontal surface is 0.3 then force of kinetic friction is :

A particle moves in $x$-$y$ plane under the influence of a force $\vec{F}$ such that its linear momentum is $\vec{p}(t) = \hat{i}\cos(kt) - \hat{j}\sin(kt)$. If $k$ is constant, the angle between $\vec{F}$ and $\vec{P}$ will be :

A body is moving unidirectionally under the influence of a constant power source. Its displacement in time t is proportional to :

A vernier callipers has 20 divisions on the vernier scale, which coincides with $19^{\text{th}}$ division on the main scale. The least count of the instrument is 0.1 mm. One main scale division is equal to ________ mm.

A satellite revolving around a planet in stationary orbit has time period 6 hours. The mass of planet is one-fourth the mass of earth. The radius orbit of planet is :

(Given = Radius of geo-stationary orbit for earth is $4.2 \times 10^4\ \mathrm{km}$)

Match List-I with List-II :

List-I	List-II
(A) A force that restores an elastic body of unit area to its original state	(I) Bulk modulus
(B) Two equal and opposite forces parallel to opposite faces	(II) Young's modulus
(C) Forces perpendicular everywhere to the surface per unit area same everywhere	(III) Stress
(D) Two equal and opposite forces perpendicular to opposite faces	(IV) Shear modulus

Choose the correct answer from the options given below :

If n is the number density and d is the diameter of the molecule, then the average distance covered by a molecule between two successive collisions (i.e. mean free path) is represented by :

The vehicles carrying inflammable fluids usually have metallic chains touching the ground :

A series LCR circuit is subjected to an ac signal of 200 V, 50 Hz. If the voltage across the inductor ($L = 10\ \mathrm{mH}$) is 31.4 V, then the current in this circuit is ________.

The ratio of heat dissipated per second through the resistance $5\ \Omega$ and $10\ \Omega$ in the circuit given below is :

a 10 V battery connected to a $20\ \Omega$ resistor in series with a parallel combination of $5\ \Omega$ and $10\ \Omega$ resistors

The electrostatic force $\left(\vec{F}_1\right)$ and magnetic force $\left(\vec{F}_2\right)$ acting on a charge q moving with velocity $v$ can be written :

Match List-I with List-II :

List-I (EM-Wave)	List-II (Wavelength Range)
(A) Infra-red	(I) $< 10^{-3}$ nm
(B) Ultraviolet	(II) 400 nm to 1 nm
(C) X-rays	(III) 1 mm to 700 nm
(D) Gamma rays	(IV) 1 nm to $10^{-3}$ nm

Choose the correct answer from the options given below :

Given below are two statements :

Statement I : When the white light passed through a prism, the red light bends lesser than yellow and violet.

Statement II : The refractive indices are different for different wavelengths in dispersive medium.

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

A galvanometer of resistance $100\ \Omega$ when connected in series with $400\ \Omega$ measures a voltage of upto 10 V. The value of resistance required to convert the galvanometer into ammeter to read upto 10 A is $x \times 10^{-2}\ \Omega$. The value of $x$ is :

Which of the following statement is not true about stopping potential $(V_0)$ ?

The angular momentum of an electron in a hydrogen atom is proportional to : (Where r is the radius of orbit of electron)

During an adiabatic process, if the pressure of a gas is found to be proportional to the cube of its absolute temperature, then the ratio of $\frac{C_P}{C_V}$ for the gas is :

The output (Y) of logic circuit given below is 0 only when :

logic circuit — inputs A and B feed an OR gate; input B and a constant input 1 feed an AND gate; the outputs of the OR gate and the AND gate feed a final OR gate whose output is Y

The maximum height reached by a projectile is 64 m. If the initial velocity is halved, the new maximum height of the projectile is ________ m.

A hollow sphere is rolling on a plane surface about its axis of symmetry. The ratio of rotational kinetic energy to its total kinetic energy is $\frac{x}{5}$. The value of $x$ is ________.

In a single slit experiment, a parallel beam of green light of wavelength 550 nm passes through a slit of width 0.20 mm. The transmitted light is collected on a screen 100 cm away. The distance of first order minima from the central maximum will be $x \times 10^{-5}$ m. The value of $x$ is :

A hydraulic press containing water has two arms with diameters as mentioned in the figure. A force of 10 N is applied on the surface of water in the thinner arm. The force required to be applied on the surface of water in the thicker arm to maintain equilibrium of water is ________ N.

a U-shaped hydraulic press — the wider arm has diameter 14 cm; the thinner arm has diameter 1.4 cm with a 10 N force applied downward on it

A sonometer wire of resonating length 90 cm has a fundamental frequency of 400 Hz when kept under some tension. The resonating length of the wire with fundamental frequency of 600 Hz under same tension ________ cm.

A wire of resistance $20\ \Omega$ is divided into 10 equal parts, resulting pairs. A combination of two parts are connected in parallel and so on. Now resulting pairs of parallel combination are connected in series. The equivalent resistance of final combination is ________ $\Omega$.

A solenoid of length 0.5 m has a radius of 1 cm and is made up of 'm' number of turns. It carries a current of 5 A. If the magnitude of the magnetic field inside the solenoid is $6.28 \times 10^{-3}\ \mathrm{T}$ then the value of m is ________.

The electric field at point p due to an electric dipole is E. The electric field at point R on equitorial line will be $\frac{E}{x}$. The value of $x$ :

a dipole with $-q$ and $+q$ on a horizontal axis about origin O; point p lies on the axial line at distance r from O; point Q lies on the equatorial (perpendicular) line at distance r from O and point R at distance 2r from O

The current in an inductor is given by $I = (3t + 8)$ where t is in second. The magnitude of induced emf produced in the inductor is 12 mV. The self-inductance of the inductor ________ mH.

The shortest wavelength of the spectral lines in the Lyman series of hydrogen spectrum is $915\ \mathrm{\mathring{A}}$. The longest wavelength of spectral lines in the Balmer series will be ________ $\mathrm{\mathring{A}}$.