JEE Main Physics - January 22, 2025 (Shift 1)

A parallel plate capacitor with capacitance 40µF is connected to a 100V power supply. When the space between the plates is filled with a dielectric material of dielectric constant k=2, the extra charge stored and the change in electrostatic energy are 4 mC and 0.2J respectively.

The moment of inertia of a uniform circular disc of radius 'R' and mass 'm' rotating about an axis perpendicular to its plane and passing through its center is (1/2)mR^2. When a smaller circular part of radius R/2 is removed, the moment of inertia of the remaining part is calculated by subtracting the moment of inertia of the removed part from the original disc's moment of inertia.

In the hydrogen atom, the ratio of the de-Broglie wavelength of an electron in the ground state (n=1) to its wavelength in the third excited state (n=4) is 1:4. This relationship arises due to the quantization of energy levels in the atom and the dependence of de-Broglie wavelength on momentum.

The dimensions of the quantity (1/μ0) are [AL⁻¹]. This can be derived using the relationship between magnetic permeability (μ0), current (I), length (L), and magnetic field (B) (B = (μ0 * I)/(2πL)).

When a concentric spherical mass (M/7) is removed from a solid sphere of mass 'M' and radius 'R', the new gravitational force on a point mass placed at a distance 2R from the center is 6F/7. This is because the force depends on the mass of the sphere enclosed within the point mass's distance. You can use the shell theorem.

In Vernier calipers, one Vernier scale division (VSD) is smaller than one main scale division (MSD). Vernier constant is calculated as one MSD divided by the number of VSDs.

The ratio of kinetic energies of the bob at points B and C in the given scenario is 2:1. This is because the potential energy at point B is converted to kinetic energy at point C, where the string becomes slack.

Converting 10^-3 kg of ice at -10°C to steam at 110°C requires a total heat of 730 calories. This involves multiple steps: melting the ice, raising the temperature of the water, and vaporizing the water.

For a thin convex lens (refractive index μ), a point object placed at a distance R/(2μ-1) from the lens will form an image coinciding with the object itself. This occurs due to the combined effect of refraction and reflection from the polished back surface of the lens.

An electron entering a uniform electric field between two parallel plates experiences a force that accelerates it in the vertical direction. Given the electric field strength, the electron's initial horizontal velocity, and the distance travelled in the field, the vertical component of its velocity can be calculated using kinematic equations.

Photoelectric effect occurs when light of sufficient energy (greater than the work function of the metal) is incident on a metal surface. In this case, the wavelength of the light is below the threshold wavelength required for photoelectric emission for Li but not for Cs. Therefore, photoelectric effect is only possible for Cs.

The frequency of the 9th harmonic of a closed organ pipe is equal to the frequency of the 4th harmonic of an open organ pipe when both are filled with gases having the same bulk modulus but different densities. This is because the frequency is determined by the length of the pipe and the speed of sound, which is dependent on the density of the gas.

The ratio of gravitational force (F1) on a point mass at a distance 2R from the center of a uniform solid sphere to the force (F2) after removing a spherical part of radius R/3 is 12:11. Use the concept of gravitational force due to a spherical shell.

The energy radiated by a spherical blackbody is proportional to its surface area and the fourth power of its absolute temperature. Therefore, the energy radiated by the larger body, with four times the surface area and twice the temperature, is 64 times that of the smaller body.

In Young's double-slit experiment, when performed in an optically denser medium, the consecutive fringes come closer because the speed of light reduces while the frequency remains constant. This results in a shorter wavelength, leading to a smaller fringe spacing.

In the given circuit, with a jockey placed at the middle point of the 1Ω resistor, the current flowing through the circuit is 1A. This can be calculated through the application of Kirchhoff's laws and analyzing the equivalent resistance of the circuit.

The lanthanide ion Gd³⁺ has 7 electrons in its outermost shell. This is because Gadolinium (Gd) has an electronic configuration of [Xe] 4f⁷ 5d¹ 6s² and the +3 oxidation state removes the 5d¹ and 6s² electrons, leaving 7 electrons in the 4f subshell.

Among the given compounds, I₃⁻, NO⁺, BeCl₂, N₃⁻, and XeF₂ are linear. Linearity arises from the hybridization of central atoms and the absence of lone pairs on the central atom.

The percentage of chlorine in an organic compound can be determined by analyzing the weight of AgCl precipitate formed. In this case, the mass of AgCl (143.5g) corresponds to 35.5g of chlorine, which is 19.72% of the organic compound's weight.

Electrolysis of concentrated sulfuric acid (H₂SO₄) produces peroxodisulfuric acid (H₂S₂O₈). This process involves the oxidation of sulfate ions at the anode.

Among the given options, Al < Mg < B < N is an incorrect order of electronegativity. The correct order is Mg < Be < B < N. Electronegativity generally increases across a period and decreases down a group.

The statement that the decay constant does not depend on temperature is not true for radioactive decay. The decay constant remains unaffected by temperature. Half-life is indeed related to the rate constant by the equation half-life = (ln2)/rate constant. The amount of radioactive substance remaining after three half-lives is indeed 1/8th of the original amount.

The order of increasing boiling points for the given solutions is 10⁻⁴ NaCl < 10⁻³ NaCl < 10⁻² NaCl < 10⁻⁴ Urea. This is because boiling point elevation is directly proportional to the molality of the solution, and ionic compounds dissociate to produce a higher number of particles in solution compared to urea.

Ascorbic acid, also known as Vitamin C, is an organic acid that acts as a vitamin. It is essential for various biological processes, including collagen synthesis and immunity.

The given molecule (CH₃-CH-CH=CH-CH₃, with OH on the second carbon) can have 4 different stereoisomers. This is because the molecule contains both a chiral center (the carbon with the OH attached) and a double bond, resulting in cis/trans isomers.

The IUPAC name of the given compound is 6-methoxy-2,5-dimethyl-6-oxohexanoic acid. This name reflects the presence of a methoxy group, two methyl groups, and a ketone group in the hexanoic acid molecule.

The statement that the melting point of cis-2-butene is greater than trans-2-butene is incorrect. Trans-2-butene has a higher melting point because its molecules can pack more closely together due to the linear arrangement of the substituents. Cis-2-butene molecules are less stable due to steric interactions.

The molecular weight of compound A, based on the given information, is 154. This can be determined by analyzing the fragmentation pattern in the mass spectrum and considering the molecular fragments and their masses.

The complex [NiCl₄]²⁻ has a +2 charge on the nickel (Ni) metal and is tetrahedral in shape. The Ni²⁺ ion has a d⁸ electronic configuration, and the four chloride (Cl⁻) ligands result in a tetrahedral geometry due to the favorable bonding interactions and electron repulsion.

The correct decreasing order of electronegativity is F > Cl > Br > I. Electronegativity generally increases across a period and decreases down a group in the periodic table.

Among the given ions (Al³⁺, Mg²⁺, F⁻, and Na⁺), F⁻ has the largest size. This is because anions are larger than their corresponding neutral atoms due to the addition of electrons, and the size of ions generally decreases across a period and increases down a group.

The equilibrium constant (Kp) for the given reaction (CO₂(g) + C(s) ⇌ 2CO(g)) is 0.4 atm. This can be calculated by considering the partial pressures of CO₂ and CO at equilibrium and using the equilibrium constant expression for the reaction.

CH₃-O-CH₂-Cl undergoes nucleophilic substitution via SN1 mechanism in a protic medium. The carbon attached to chlorine is a primary carbon, but the presence of the oxygen atom adjacent to it stabilizes the intermediate carbocation, favoring the SN1 mechanism. The Cl will not undergo nucleophilic substitution via SN2 mechanism easily as the presence of the oxygen atom makes the carbon susceptible to SN1.

The de-Broglie wavelength of an electron in the 3rd excited state of He⁺ is 6.64 Å. This value can be calculated using the formula λ = h/p, where h is Planck's constant and p is momentum, which is related to the principal quantum number (n) and the ionization energy for the He⁺ ion.

The ability of a material to store electrical energy when a potential difference is applied across it. Measured in Farads (F).

A non-conducting material that increases the capacitance of a capacitor when placed between its plates. It reduces the electric field strength by polarizing itself.

The measure of an object's resistance to rotational motion. It depends on the object's mass distribution and the axis of rotation.

The wavelength of a particle, such as an electron, determined by its momentum. It describes the wave-like nature of particles.

The ability of a material to support the formation of magnetic fields. Measured in Henries (H).

A mathematical principle that states that a spherically symmetric mass distribution exerts the same gravitational force on an external point mass as if all its mass were concentrated at its center. The force is independent of the mass outside the point mass's distance.

An instrument used to measure objects with high precision, using a vernier scale that divides a main scale division into smaller units.

The energy associated with an object's motion, depending on its mass and velocity. Measured in Joules (J).

The process of converting a substance from one physical state to another, primarily involving changes in intermolecular forces and energy.

A transparent object that refracts light, focusing it to a point or spreading it out. Used in various optical devices.

A force that acts on charged particles in an electric field, causing acceleration. Measured in Newtons (N).

A series of frequencies produced by a vibrating object, with the fundamental frequency being the lowest and harmonics being multiples of it.

A type of nucleophilic substitution reaction where the leaving group departs first to form a carbocation intermediate, followed by the attack of the nucleophile.

A type of nucleophilic substitution reaction where the nucleophile attacks the carbon directly, leading to a concerted one-step process.

The energy required to remove an electron from an atom in its gaseous state. Measured in electron volts (eV).

A specific type of chemical reaction involving the transfer of electrons from a reducing agent to an oxidizing agent.

An ionic compound that is formed when a metal atom donates one or more electrons to a nonmetal atom.

The process of breaking down a molecule into smaller components by adding water.

A compound that releases hydrogen ions (H+) when dissolved in water.

A compound that releases hydroxide ions (OH-) when dissolved in water.

A substance that increases the rate of a chemical reaction without being consumed in the process.

The smallest unit of a chemical element, consisting of a nucleus containing protons and neutrons, and surrounded by electrons.

A subatomic particle that carries a positive charge and resides within the nucleus of an atom.

A subatomic particle that carries a negative charge and orbits the nucleus of an atom.

A subatomic particle that carries no charge and resides within the nucleus of an atom.

A group of atoms held together by chemical bonds.

The attractive force that holds atoms together in a molecule.

A measure of the tendency of an atom to attract electrons in a chemical bond.

The process of transforming a substance from a liquid to a gas.