JEE Main 2025 Jan 28 Shift 2 — Physics

a bar magnet with poles S and N, total length $2l$, and a field point P located on the perpendicular bisector at distance $d$ from the centre of the magnet

A bar magnet has total length $2l = 20$ units and the field point P is at a distance $d = 10$ units from the centre of the magnet. If the relative uncertainty of length measurement is 1%, then uncertainty of the magnetic field at point P is :

Match List - I with List - II.

List - I	List - II
(A) Angular Impulse	(I) $[\mathrm{M^0 L^2 T^{-2}}]$
(B) Latent Heat	(II) $[\mathrm{M L^2 T^{-3} A^{-1}}]$
(C) Electrical resistivity	(III) $[\mathrm{M L^2 T^{-1}}]$
(D) Electromotive force	(IV) $[\mathrm{M L^3 T^{-3} A^{-2}}]$

Choose the correct answer from the options given below :

The velocity-time graph of an object moving along a straight line is shown in figure. What is the distance covered by the object from $t = 0$ to $t = 4\,\mathrm{s}$?

velocity-time graph; $v$ (in $\mathrm{ms^{-1}}$) rises linearly from O at $t=0$ to $10$ at point A ($t=2\,\mathrm{s}$), stays constant at $10$ from A to B ($t=4\,\mathrm{s}$), then decreases linearly to zero at $t=6\,\mathrm{s}$

Earth has mass 8 times and radius 2 times that of a planet. If the escape velocity from the earth is $11.2\,\mathrm{km/s}$, the escape velocity in $\mathrm{km/s}$ from the planet will be :

A uniform rod of mass 250 g having length 100 cm is balanced on a sharp edge at 40 cm mark. A mass of 400 g is suspended at 10 cm mark. To maintain the balance of the rod, the mass to be suspended at 90 cm mark, is

A body of mass 4 kg is placed on a plane at a point P having coordinate $(3, 4)$ m. Under the action of force $\vec{F} = \left(2\hat{i} + 3\hat{j}\right)\,\mathrm{N}$, it moves to a new point Q having coordinates $(6, 10)$ m in 4 sec. The average power and instantaneous power at the end of 4 sec are in the ratio of :

A balloon and its content having mass M is moving up with an acceleration 'a'. The mass that must be released from the content so that the balloon starts moving up with an acceleration '3a' will be

(Take 'g' as acceleration due to gravity)

A 400 g solid cube having an edge of length 10 cm floats in water. How much volume of the cube is outside the water?

(Given : density of water $= 1000\,\mathrm{kg\,m^{-3}}$)

The kinetic energy of translation of the molecules in 50 g of $\mathrm{CO_2}$ gas at 17°C is

The ratio of vapour densities of two gases at the same temperature is $\dfrac{4}{25}$, then the ratio of r.m.s. velocities will be :

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) : Knowing initial position $x_0$ and initial momentum $p_0$ is enough to determine the position and momentum at any time t for a simple harmonic motion with a given angular frequency $\omega$.

Reason (R) : The amplitude and phase can be expressed in terms of $x_0$ and $p_0$.

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

A parallel plate capacitor of capacitance $1\,\mu\mathrm{F}$ is charged to a potential difference of 20 V. The distance between plates is $1\,\mu\mathrm{m}$. The energy density between plates of capacitor is.

an infinite straight wire carrying current I along the horizontal, which forms a circular bend (loop) of radius $a$ around the origin O; the arc subtends the region above and to the left of O, and the two straight portions extend to infinity on the right

An infinite wire has a circular bend of radius $a$, and carrying a current I as shown in figure. The magnitude of magnetic field at the origin O of the arc is given by :

A uniform magnetic field of 0.4 T acts perpendicular to a circular copper disc 20 cm in radius. The disc is having a uniform angular velocity of $10\pi\,\mathrm{rad\,s^{-1}}$ about an axis through its centre and perpendicular to the disc. What is the potential difference developed between the axis of the disc and the rim? ($\pi = 3.14$)

The magnetic field of an E.M. wave is given by $\vec{B} = \left(\dfrac{\sqrt{3}}{2}\hat{i} + \dfrac{1}{2}\hat{j}\right)30\sin\left[\omega\left(t - \dfrac{z}{c}\right)\right]$ (S.I. Units).

The corresponding electric field in S.I. units is :

In a long glass tube, mixture of two liquids A and B with refractive indices 1.3 and 1.4 respectively, forms a convex refractive meniscus towards A. If an object placed at 13 cm from the vertex of the meniscus in A forms an image with a magnification of '$-2$' then the radius of curvature of meniscus is :

A concave mirror produces an image of an object such that the distance between the object and image is 20 cm. If the magnification of the image is '$-3$', then the magnitude of the radius of curvature of the mirror is :

The frequency of revolution of the electron in Bohr's orbit varies with n, where n is the principal quantum number, as :

Which of the following phenomena can not be explained by wave theory of light?

an AC source $V = V_0\sin\omega t$ connected in a circuit; a resistor R is in parallel between terminals A (top) and B (bottom), and a diode is in the lower branch of the loop

In the circuit shown here, assuming threshold voltage of diode is negligibly small, then voltage $V_{AB}$ is correctly represented by :

The volume contraction of a solid copper cube of edge length 10 cm, when subjected to a hydraulic pressure of $7 \times 10^6\,\mathrm{Pa}$, would be __________ $\mathrm{mm^3}$.

(Given bulk modulus of copper $= 1.4 \times 10^{11}\,\mathrm{N\,m^{-2}}$)

An electric dipole of dipole moment $6 \times 10^{-6}\,\mathrm{Cm}$ is placed in uniform electric field of magnitude $10^6\,\mathrm{V/m}$. Initially, the dipole moment is parallel to electric field. The work that needs to be done on the dipole to make its dipole moment opposite to the field, will be __________ J.

The value of current I in the electrical circuit as given below, when potential at A is equal to the potential at B, will be __________ A.

a Wheatstone-bridge-like network. Current I enters a node splitting into two branches: the top branch has $10\,\Omega$ then node A then $20\,\Omega$; the bottom branch has R then node B then $40\,\Omega$. A $30\,\Omega$ resistor connects A to B (bridge arm). The two branches recombine and current I exits. The network is driven by a 40 V battery with key K.

a conducting bar moving on two conducting rails that form a V-shape (vertex at bottom); a constant magnetic field B is directed into the page (shown by × symbols)

A conducting bar moves on two conducting rails as shown in the figure. A constant magnetic field B exists into the page. The bar starts to move from the vertex at time $t = 0$ with a constant velocity. If the induced EMF is $E \propto t^n$, then value of n is __________.

A thin transparent film with refractive index 1.4, is held on circular ring of radius 1.8 cm. The fluid in the film evaporates such that transmission through the film at wavelength 560 nm goes to a minimum every 12 seconds. Assuming that the film is flat on its two sides, the rate of evaporation is __________ $\pi \times 10^{-13}\,\mathrm{m^3/s}$.