JEE Main 2025 Jan 22 Shift 2 — Physics

Which one of the following is the correct dimensional formula for the capacitance in F ? M, L, T and C stand for unit of mass, length, time and charge,

The maximum percentage error in the measurment of density of a wire is

[Given, mass of wire $= (0.60 \pm 0.003)\,\mathrm{g}$

radius of wire $= (0.50 \pm 0.01)\,\mathrm{cm}$

length of wire $= (10.00 \pm 0.05)\,\mathrm{cm}$]

The torque due to the force $\left(2\hat{i} + \hat{j} + 2\hat{k}\right)$ about the origin, acting on a particle whose position vector is $\left(\hat{i} + \hat{j} + \hat{k}\right)$, would be

A ball of mass 100 g is projected with velocity 20 m/s at $60^{\circ}$ with horizontal. The decrease in kinetic energy of the ball during the motion from point of projection to highest point is

A body of mass 100 g is moving in circular path of radius 2 m on vertical plane as shown in figure. The velocity of the body at point A is 10 m/s. The ratio of its kinetic energies at point B and C is :

a vertical circle with centre O; A is the lowest point, D the highest point; C lies above the horizontal diameter and B below it, with OB making $30^{\circ}$ with the horizontal and angle between OC and OB equal to $90^{\circ}$

(Take acceleration due to gravity as $10\ \mathrm{m/s^2}$)

A force $\vec{F} = 2\hat{i} + b\hat{j} + \hat{k}$ is applied on a particle and it undergoes a displacement $\hat{i} - 2\hat{j} - \hat{k}$. What will be the value of b, if work done on the particle is zero.

a tapering tube; water enters the wider end marked (1) and leaves the narrower end marked (2)

A tube of length L is shown in the figure. The radius of cross section at the point (1) is 2 cm and at the point (2) is 1 cm, respectively. If the velocity of water entering at point (1) is 2 m/s, then velocity of water leaving the point (2) will be

A small rigid spherical ball of mass M is dropped in a long vertical tube containing glycerine. The velocity of the ball becomes constant after some time. If the density of glycerine is half of the density of the ball, then the viscous force acting on the ball will be

(consider g as acceleration due to gravity)

For a diatomic gas, if $\gamma_1 = \left(\frac{C_p}{C_v}\right)$ for rigid molecules and $\gamma_2 = \left(\frac{C_p}{C_v}\right)$ for another diatomic molecules, but also having vibrational modes. Then, which one of the following options is correct ?

($C_p$ and $C_v$ are specific heats of the gas at constant pressure and volume)

Given are statements for certain thermodynamic variables,

(A) Internal energy, volume (V) and mass (M) are extensive variables.

(B) Pressure (P), temperature (T) and density ($\rho$) are intensive variables.

(C) Volume (V), temperature (T) and density ($\rho$) are intensive variables.

(D) Mass (M), temperature (T) and internal energy are extensive variables.

Choose the correct answer from the options given below :

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

Assertion (A) : A simple pendulum is taken to a planet of mass and radius, 4 times and 2 times, respectively, than the Earth. The time period of the pendulum remains same on earth and the planet.

Reason (R) : The mass of the pendulum remains unchanged at Earth and the other planet.

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

For a short dipole placed at origin O, the dipole moment P is along $x$-axis, as shown in the figure. If the electric potential and electric field at A are $V_0$ and $E_0$, respectively, then the correct combination of the electric potential and electric field, respectively, at point B on the $y$-axis is given by

dipole P at origin O pointing along the positive $x$-axis; point A on the $x$-axis at distance r from O; point B on the $y$-axis at distance 2r from O

A rectangular metallic loop is moving out of a region of uniform magnetic field into a magnetic field-free region with a constant velocity. When the loop is partially inside the magnetic field, the plot of induced emf ($\varepsilon$) with time (t) is given by :

A series LCR circuit is connected to an alternating source of emf E. The current amplitude at resonant frequency is $I_0$. If the value of resistance R becomes twice of its initial value then amplitude of current at resonance will be

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

Assertion (A) : In Young's double slit experiment, the fringes produced by red light are closer as compared to those produced by blue light.

Reason (R) : The fringe width is directly proportional to the wavelength of light.

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

logic circuit — inputs A and B are fed directly to one AND gate; A and B are also fed through NOT gates to a second AND gate; the outputs of both AND gates are fed to a gate G whose output is Y

A	B	Y
0	0	1
0	1	0
1	0	0
1	1	1

To obtain the given truth table, the following logic gate should be placed at G :

A tube of length 1m is filled completely with an ideal liquid of mass 2M, and closed at both ends. The tube is rotated uniformly in horizontal plane about one of its ends. If the force exerted by the liquid at the other end is F then angular velocity of the tube is $\sqrt{\dfrac{F}{\alpha M}}$ in SI unit. The value of $\alpha$ is __________.

A proton is moving undeflected in a region of crossed electric and magnetic fields at a constant speed of $2 \times 10^5\ \mathrm{ms^{-1}}$. When the electric field is switched off, the proton moves along a circular path of radius 2 cm. The magnitude of electric field is $x \times 10^4\ \mathrm{N/C}$. The value of $x$ is __________. Take the mass of the proton $= 1.6 \times 10^{-27}\ \mathrm{kg}$.