JEE Main 2021 Physics Paper: 27 Jul, Shift 2

A 100$\Omega$ resistance, a 0.1 $\mu$F capacitor and an inductor are connected in series across a 250 V supply at variable frequency. Calculate the value of inductance of inductor at which resonance will occur. Given that the resonant frequency is 60 Hz.

The K$\alpha$ X-ray of molybdenum has wavelength 0.071 nm. If the energy of a molybdenum atom with a K electron knocked out is 27.5 keV, the energy of this atom when an L electron is knocked out will be __________ keV. (Round off to the nearest integer)

[h = 4.14 $\times$ 10$-$15 eVs, c = 3 $\times$ 108 ms${}^{-1}$]

A simple pendulum of mass 'm', length 'l' and charge '+ q' suspended in the electric field produced by two conducting parallel plates as shown. The value of deflection of pendulum in equilibrium position will be

The resistance of a conductor at 15$^\circ$C is 16$\Omega$ and at 100$^\circ$ C is 20$\Omega$. What will be the temperature coefficient of resistance of the conductor?

For the circuit shown, the value of current at time t = 3.2 s will be _________ A.

[Voltage distribution V(t) is shown by Fig. (1) and the circuit is shown in Fig. (2)]

An electron and proton are separated by a large distance. The electron starts approaching the proton with energy 3 eV. The proton captures the electron and forms a hydrogen atom in second excited state. The resulting photon is incident on a photosensitive metal of threshold wavelength 4000$\text{\AA}$. What is the maximum kinetic energy of the emitted photoelectron?

In the given figure the magnetic flux through the loop increases according to the relation $\phi$B(t) = 10t2 + 20t, where $\phi$B is in milliwebers and t is in seconds.

The magnitude of current through R = 2$\Omega$ resistor at t = 5 s is ___________ mA.

What will be the magnitude of electric field at point O as shown in the figure? Each side of the figure is l and perpendicular to each other.

The water is filled upto height of 12 m in a tank having vertical sidewalls. A hole is made in one of the walls at a depth 'h' below the water level. The value of 'h' for which the emerging steam of water strikes the ground at the maximum range is ________ m.

The planet Mars has two moons, if one of them has a period 7 hours, 30 minutes and an orbital radius of 9.0 $\times$ 103 km. Find the mass of Mars.

$\left\{\text{Given } \frac{4\pi^2}{G} = 6 \times 10^{11}\text{ N}^{-1}\text{m}^{-2}\text{kg}^{2}\right\}$

Two identical particles of mass 1 kg each go round a circle of radius R, under the action of their mutual gravitational attraction. The angular speed of each particle is:

A particle of mass M originally at rest is subjected to a force whose direction is constant but magnitude varies with time according to the relation

$F = F_0\left[1 - \left(\frac{t-T}{T}\right)^{2}\right]$

Where F0 and T are constants. The force acts only for the time interval 2T. The velocity v of the particle after time 2T is:

Figures A and B show two long straight wires of circular cross-section (a and b with a < b), carrying current I which is uniformly distributed across the cross-section. The magnitude of magnetic field B varies with radius r and can be represented as:

Consider the following statements:

A. Atoms of each element emit characteristics spectrum.

B. According to Bohr's Postulate, an electron in a hydrogen atom, revolves in a certain stationary orbit.

C. The density of nuclear matter depends on the size of the nucleus.

D. A free neutron is stable but a free proton decay is possible.

E. Radioactivity is an indication of the instability of nuclei.

Choose the correct answer from the options given below:

An object of mass 0.5 kg is executing simple harmonic motion. It amplitude is 5 cm and time period (T) is 0.2 s. What will be the potential energy of the object at an instant $t = \frac{T}{4}\text{ s}$ starting from mean position. Assume that the initial phase of the oscillation is zero.

A particle executes simple harmonic motion represented by displacement function as x(t) = A sin($\omega$t + $\phi$)

If the position and velocity of the particle at t = 0 s are 2 cm and 2$\omega$ cm s${}^{-1}$ respectively, then its amplitude is $x\sqrt{2}$ cm where the value of x is _________________.

A swimmer wants to cross a river from point A to point B. Line AB makes an angle of 30$^\circ$ with the flow of river. Magnitude of velocity of the swimmer is same as that of the river. The angle $\theta$ with the line AB should be _________$^\circ$, so that the swimmer reaches point B.

The expected graphical representation of the variation of angle of deviation '$\delta$' with angle of incidence 'i' in a prism is:

In the given figure, two wheels P and Q are connected by a belt B. The radius of P is three times as that of Q. In case of same rotational kinetic energy, the ratio of rotational inertias $\left(\frac{I_1}{I_2}\right)$ will be x: 1. The value of x will be _____________.

Find the truth table for the function Y of A and B represented in the following figure.

Two Carnot engines A and B operate in series such that engine A absorbs heat at T1 and rejects heat to a sink at temperature T. Engine B absorbs half of the heat rejected by Engine A and rejects heat to the sink at T3. When workdone in both the cases is equal, to value of T is:

One mole of an ideal gas is taken through an adiabatic process where the temperature rises from 27$^\circ$ C to 37$^\circ$ C. If the ideal gas is composed of polyatomic molecule that has 4 vibrational modes, which of the following is true? [R = 8.314 J mol${}^{-1}$ K${}^{-1}$]

A physical quantity 'y' is represented by the formula $y = m^{2} r^{-4} g^{x} l^{-\frac{3}{2}}$

If the percentage errors found in y, m, r, l and g are 18, 1, 0.5, 4 and p respectively, then find the value of x and p.

Match List I with List II.

Choose the correct answer from the options given below

A raindrop with radius R = 0.2 mm falls from a cloud at a height h = 2000 m above the ground. Assume that the drop is spherical throughout its fall and the force of buoyance may be neglected, then the terminal speed attained by the raindrop is:

[Density of water fw = 1000 kg m${}^{-3}$ and Density of air fa = 1.2 kg m${}^{-3}$, g = 10 m/s2, Coefficient of viscosity of air = 1.8 $\times$ 10$-$5 Nsm${}^{-2}$]

The difference in the number of waves when yellow light propagates through air and vacuum columns of the same thickness is one. The thickness of the air column is ___________ mm. [Refractive index of air = 1.0003, wavelength of yellow light in vacuum = 6000 $\text{\AA}$]

Given below is the plot of a potential energy function U(x) for a system, in which a particle is in one dimensional motion, while a conservative force F(x) acts on it. Suppose that Emech = 8 J, the incorrect statement for this system is:

[ where K.E. = kinetic energy ]

An automobile of mass 'm' accelerates starting from origin and initially at rest, while the engine supplies constant power P. The position is given as a function of time by: