JEE Main 2022 Physics Paper: 28 Jun, Shift 2

In the given circuit, the magnitude of VL and VC are twice that of VR. Given that f = 50 Hz, the inductance of the coil is $\frac{1}{K\pi}$ mH. The value of K is ____________.

A capacitor C1 of capacitance 5 $\mu$F is charged to a potential of 30 V using a battery. The battery is then removed and the charged capacitor is connected to an uncharged capacitor C2 of capacitance 10 $\mu$F as shown in figure. When the switch is closed charge flows between the capacitors. At equilibrium, the charge on the capacitor C2 is __________ $\mu$C.

All resistances in figure are 1 $\Omega$ each. The value of current 'I' is $\frac{a}{5}$ A. The value of a is _________.

Resistance of the wire is measured as 2 $\Omega$ and 3 $\Omega$ at 10$^\circ$C and 30$^\circ$C respectively. Temperature co- efficient of resistance of the material of the wire is:

Let K1 and K2 be the maximum kinetic energies of photo-electrons emitted when two monochromatic beams of wavelength $\lambda$1 and $\lambda$2, respectively are incident on a metallic surface. If $\lambda$1 = 3$\lambda$2 then:

A coil is placed in a time varying magnetic field. If the number of turns in the coil were to be halved and the radius of wire doubled, the electrical power dissipated due to the current induced in the coil would be:

(Assume the coil to be short circuited.)

An EM wave propagating in x-direction has a wavelength of 8 mm. The electric field vibrating y- direction has maximum magnitude of 60 Vm${}^{-1}$. Choose the correct equations for electric and magnetic fields if the EM wave is propagating in vacuum:

Two point charges A and B of magnitude +8 $\times$ 10$-$6 C and $-$8 $\times$ 10$-$6 C respectively are placed at a distance d apart. The electric field at the middle point O between the charges is 6.4 $\times$ 104 NC${}^{-1}$. The distance 'd' between the point charges A and B is:

A liquid of density 750 kgm${}^{-3}$ flows smoothly through a horizontal pipe that tapers in cross- sectional area from A1 = 1.2 $\times$ 10$-$2 m2 to A2 = $\frac{A_1}{2}$. The pressure difference between the wide and narrow sections of the pipe is 4500 Pa. The rate of flow of liquid is ___________ $\times$ 10$-$3 m3s${}^{-1}$.

Water falls from a 40 m high dam at the rate of 9 $\times$ 104 kg per hour. Fifty percentage of gravitational potential energy can be converted into electrical energy. Using this hydroelectric energy number of 100 W lamps, that can be lit, is:

(Take g = 10 ms${}^{-2}$)

Two objects of equal masses placed at certain distance from each other attracts each other with a force of F. If one-third mass of one object is transferred to the other object, then the new force will be:

What will be the effect on the root mean square velocity of oxygen molecules if the temperature is doubled and oxygen molecule dissociates into atomic oxygen?

The space inside a straight current carrying solenoid is filled with a magnetic material having magnetic susceptibility equal to 1.2 $\times$ 10$-$5. What is fractional increase in the magnetic field inside solenoid with respect to air as medium inside the solenoid?

A car covers AB distance with first one-third at velocity v1 ms${}^{-1}$, second one-third at v2 ms${}^{-1}$ and last one-third at v3 ms${}^{-1}$. If v3 = 3v1, v2 = 2v1 and v1 = 11 ms${}^{-1}$ then the average velocity of the car is _____________ ms______1.

Two parallel, long wires are kept 0.20 m apart in vacuum, each carrying current of x A in the same direction. If the force of attraction per meter of each wire is 2 $\times$ 10$-$6 N, then the value of x is approximately:

Following statements related to radioactivity are given below:

(A) Radioactivity is a random and spontaneous process and is dependent on physical and chemical conditions.

(B) The number of un-decayed nuclei in the radioactive sample decays exponentially with time. (C) Slope of the graph of loge (no. of undecayed nuclei) Vs. time represents the reciprocal of mean life time ($\tau$).

(D) Product of decay constant ($\lambda$) and half-life time (T1/2) is not constant.

Choose the most appropriate answer from the options given below:

A ball is spun with angular acceleration $\alpha$ = 6t2 $-$ 2t where t is in second and $\alpha$ is in rads${}^{-2}$. At t = 0, the ball has angular velocity of 10 rads${}^{-1}$ and angular position of 4 rad. The most appropriate expression for the angular position of the ball is:

A uniform disc with mass M = 4 kg and radius R = 10 cm is mounted on a fixed horizontal axle as shown in figure. A block with mass m = 2 kg hangs from a massless cord that is wrapped around the rim of the disc. During the fall of the block, the cord does not slip and there is no friction at the axle. The tension in the cord is ____________ N.

(Take g = 10 ms${}^{-2}$)

A $\sqrt{34}$ m long ladder weighing 10 kg leans on a frictionless wall. Its feet rest on the floor 3 m away from the wall as shown in the figure. If Ff and Fw are the reaction forces of the floor and the wall, then ratio of $F_w/F_f$ will be:

(Use g = 10 m/s2.)

In the given circuit the input voltage Vin is shown in figure. The cut-in voltage of p-n junction diode (D1 or D2) is 0.6 V. Which of the following output voltage (V0) waveform across the diode is correct?

A zener of breakdown voltage Vz = 8 V and maximum zener current, IZM = 10 mA is subjected to an input voltage Vi = 10 V with series resistance R = 100 $\Omega$. In the given circuit RL represents the variable load resistance. The ratio of maximum and minimum value of RL is _____________.

A sample of an ideal gas is taken through the cyclic process ABCA as shown in figure. It absorbs, 40 J of heat during the part AB, no heat during BC and rejects 60 J of heat during CA. A work of 50 J is done on the gas during the part BC. The internal energy of the gas at A is 1560 J. The workdone by the gas during the part CA is:

Velocity (v) and acceleration (a) in two systems of units 1 and 2 are related as $v_2 = \frac{n}{m^2}v_1$ and $a_2 = \frac{a_1}{mn}$ respectively. Here m and n are constants. The relations for distance and time in two systems respectively are:

A student in the laboratory measures thickness of a wire using screw gauge. The readings are 1.22 mm, 1.23 mm, 1.19 mm and 1.20 mm. The percentage error is $\frac{x}{121}\%$. The value of x is ____________.

A water drop of radius 1 $\mu$m falls in a situation where the effect of buoyant force is negligible. Co- efficient of viscosity of air is 1.8 $\times$ 10$-$5 Nsm${}^{-2}$ and its density is negligible as compared to that of water 106 gm${}^{-3}$. Terminal velocity of the water drop is:

(Take acceleration due to gravity = 10 ms${}^{-2}$)

A tuning fork of frequency 340 Hz resonates in the fundamental mode with an air column of length 125 cm in a cylindrical tube closed at one end. When water is slowly poured in it, the minimum height of water required for observing resonance once again is ___________ cm.

(Velocity of sound in air is 340 ms${}^{-1}$)

In a Young's double slit experiment, an angular width of the fringe is 0.35$^\circ$ on a screen placed at 2 m away for particular wavelength of 450 nm. The angular width of the fringe, when whole system is immersed in a medium of refractive index 7/5, is $\frac{1}{\alpha}$. The value of $\alpha$ is ___________.

In Young's double slit experiment performed using a monochromatic light of wavelength $\lambda$, when a glass plate ($\mu$ = 1.5) of thickness x$\lambda$ is introduced in the path of the one of the interfering beams, the intensity at the position where the central maximum occurred previously remains unchanged. The value of x will be:

A block of mass 2 kg moving on a horizontal surface with speed of 4 ms${}^{-1}$ enters a rough surface ranging from x = 0.5 m to x = 1.5 m. The retarding force in this range of rough surface is related to distance by F = $-$ kx where k = 12 Nm${}^{-1}$. The speed of the block as it just crosses the rough surface will be: