JEE Main 2025 Jan 23 Shift 1 — Physics

A light hollow cube of side length 10 cm and mass 10g, is floating in water. It is pushed down and released to execute simple harmonic oscillations. The time period of oscillations is $y\pi \times 10^{-2}$ s, where the value of $y$ is

(Acceleration due to gravity, $g = 10\ \mathrm{m/s^2}$, density of water $= 10^3\ \mathrm{kg/m^3}$)

A point particle of charge $Q$ is placed at $P$ along the axis of an electric dipole 1 at a distance $r$, as shown in the figure. The point $P$ is also at a distance $r$ from the equatorial plane of a second electric dipole 2. The dipoles are made of opposite charges $q$ separated by a distance $2a$. For the charge particle at $P$ not to experience any net force, which of the following correctly describes the situation?

dipole 1 (charges $+q$ and $-q$ separated by $2a$) lies along a horizontal axis with point P on this axis at distance $r$ from it; dipole 2 (charges $+q$ and $-q$ separated by $2a$) lies horizontally below P, with P at distance $r$ on its equatorial (perpendicular bisector) line

Regarding self-inductance:

A. The self-inductance of the coil depends on its geometry.

B. Self-inductance does not depend on the permeability of the medium.

C. Self-induced e.m.f. opposes any change in the current in a circuit.

D. Self-inductance is electromagnetic analogue of mass in mechanics.

E. Work needs to be done against self-induced e.m.f. in establishing the current.

Choose the correct answer from the options given below:

Consider a moving coil galvanomenter (MCG):

A. The torsional constant in moving coil galvanometer has dimentions $[\mathrm{ML^2T^{-2}}]$

B. Increasing the current sensitivity may not necessarily increase the voltage sensitivity.

C. If we increase number of turns (N) to its double (2N), then the voltage sensitivity doubles.

D. MCG can be converted into an ammeter by introducing a shunt resistance of large value in parallel with galvanometer.

E. Current sensitivity of MCG depends inversely on number of turns of coil.

Choose the correct answer from the options given below:

The electric field of an electromagnetic wave in free space is $$\vec{E} = 57 \cos\left[7.5\times10^{6}\,\mathrm{t} - 5\times10^{-3}\left(3x+4y\right)\right]\left(4\hat{i}-3\hat{j}\right)\ \mathrm{N/C}.$$ The associated magnetic field in Tesla is

Given a thin convex lens (refractive index $\mu_2$), kept in a liquid (refractive index $\mu_1$, $\mu_1 < \mu_2$) having radii of curvatures $|R_1|$ and $|R_2|$. Its second surface is silver polished. Where should an object be placed on the optic axis so that a real and inverted image is formed at the same place?

What is the lateral shift of a ray refracted through a parallel-sided glass slab of thickness 'h' in terms of the angle of incidence 'i' and angle of refraction 'r', if the glass slab is placed in air medium?

A spherical surface of radius of curvature R, separates air from glass (refractive index = 1.5). The centre of curvature is in the glass medium. A point object 'O' placed in air on the optic axis of the surface, so that its real image is formed at 'I' inside glass. The line OI intersects the spherical surface at P and PO = PI. The distance PO equals to

A sub-atomic particle of mass $10^{-30}$ kg is moving with a velocity $2.21 \times 10^{6}$ m/s. Under the matter wave consideration, the particle will behave closely like _____. ($h = 6.63 \times 10^{-34}$ J.s)

The decay constant of a radioactive nucleus $\mathrm{n_2}$ is 3 times that of another radioactive nucleus $\mathrm{n_1}$. If the initial number of both nuclei is the same, what is the ratio of the number of nuclei of $\mathrm{n_2}$ to the number of nuclei of $\mathrm{n_1}$ after one half-life of $\mathrm{n_1}$?

Refer to the circuit diagram given in the figure. which of the following observations are correct?

A. Total resistance of circuit is 6 $\Omega$

B. Current in Ammeter is 1A

C. Potential across AB is 4 Volts.

D. Potential across CD is 4 Volts

E. Total resistance of the circuit is 8 $\Omega$.

Choose the correct answer from the options given below:

circuit with battery E = 6 V in series with an ammeter leading to node C; a 4 $\Omega$ resistor from C down to node D; from D one branch has a 4 $\Omega$ resistor to the bottom rail and a second branch passes through a forward-biased diode to node A, then a 4 $\Omega$ resistor from A down to node B on the bottom rail

Two particles are located at equal distance from origin. The position vectors of those are represented by $\vec{A} = 2\hat{i} + 3n\hat{j} + 2\hat{k}$ and $\vec{B} = 2\hat{i} - 2\hat{j} + 4p\hat{k}$, respectively. If both the vectors are at right angle to each other, the value of $n^{-1}$ is _____.

A force $f = x^2y\hat{i} + y^2\hat{j}$ acts on a particle in a plane $x + y = 10$. The work done by this force during a displacement from $(0, 0)$ to $(4\,\mathrm{m}, 2\,\mathrm{m})$ is _____ Joule (round off to the nearest integer)

An ideal gas, initially at $0\,^{\circ}\mathrm{C}$ temperature, is suddenly compressed to one quarter of its volume. If the ratio of specific heat at constant pressure to the specific heat at constant volume is $3/2$, the change in temperature due to the thermodynamic process is _____ K.

In the given circuit the sliding contact is pulled outwards such that electric current in the circuit changes at the rate of 8 A/s. At an instant when R is 12 $\Omega$, the value of the current in the circuit will be _____ A.

series circuit with a 12 V battery, a 3 H inductor, and a rheostat R (resistor with sliding contact)

A positive ion A and a negative ion B has charges $6.67 \times 10^{-19}$ C and $9.6 \times 10^{-10}$ C, and masses $19.2 \times 10^{-27}$ kg and $9 \times 10^{-27}$ kg respectively. At an instant, the ions are separated by a certain distance. At that instant the ratio of the magnitudes of electrostat_____

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