JEE Main 2022 Physics Paper: 30 Jul, Shift 2

In an A.C circuit, V & I are given by $V = 250\sin(100t)$ volt and $I = 10\sin\left(100t + \frac{\pi}{3}\right)\text{ A}$ respectively The power dissipated in the circuit is:

A sinusoidal voltage $V(t) = 200\sin 2000t$ volt is applied to a series LCR circuit in which $L = 10\text{ mH},\ C = 25\ \mu\text{F}$ and $R = 100\ \Omega$. The impedance of the circuit is _______ $\Omega$

A nuclear physicist performed an experiment on the scattering of alpha particles by thin metal foil of gold. The alpha particles were accelerated up to kinetic energy 3.2 Mev. The estimation of the radius of the nucleus of gold element ($Z = 79$) by him is _______ $\times 10^{-16}\text{ m}$

(Take $\frac{1}{4\pi\epsilon_0} = 9 \times 10^{9}\ \frac{\text{N m}^2}{\text{C}^2}$)

Using Boh'r model of quantization of angular momentum the relation between the radius 'r' of the $n$th allowed orbit of quantum number 'n' for an electron in hydrogen atom is:

Combination of four parallel plate air capacitors is shown in figure. Separation between the plate $P_1$ & $P_2$ is $\frac{d}{3}$ and separation between the plates $P_2$ and $P_3$ is $d$. The equivalent capacitance of the configuration is _______ $\mu\text{F}$.

(Given $\frac{\epsilon_0 A}{d} = 4\ \mu\text{F}$. Where A=Area of plates)

A mass of $0.5\text{ kg}$ is attached to one end of a massless spring whose natural length is $1\text{ m}$ and spring constant is $800\text{ N/m}$ The other end of the spring is fixed while the mass moves in a circular path in a horizontal plane with an angular speed of $20\text{ rad/s}$. The extension in the length of the spring will be:

A cell sends a current through a resistance $4\ \Omega$ for time $t$ and sends current through another resistance $16\ \Omega$ for the same time $t$. If the same amount of heat is developed in both the resistances, then the internal resistance of the cell is _____ $\Omega$

The current I drawn out of the battery connected in the given circuit is:

The de Broglie wavelength associated with an electron, accelerated through a potential difference of $15056\text{ V}$, is:

A plane electromagnetic wave propagating in free space has amplitude of electric field of $900\ \frac{\text{N}}{\text{C}}$. The amplitude of magnetic field will be :__________

A charge $q$ is uniformly distributed along the length $L$ of a rod. It is then bent in the shape of a semicircle. The magnitude of electric field at the centre of semicircle will be:

The time period of X planet of our solar system is $8$ years. The distance of earth from the sun is $1.5 \times 10^{11}\text{ m}$. The distance of the X planet from the sun will be:

If the r.m.s speed of oxygen at room temperature is $\sqrt{56}\text{ m/s}$. The r.m.s speed of nitrogen at the same temperature is ________.

A bullet of mass $10$ gram is fired with velocity of $100\text{ m/s}$ from the gun of mass $1\text{ kg}$. Recoil speed of the gun is:

A block of mass M is attached to a wire. The upper part of wire is made of steel and lower part of wire of copper ( as shown in figure ). Both parts have the same area of cross section. Neglecting the mass of wires, the ratio of longitudinal strain developed in steel and copper wires is: ( Given, Young's modulus of steel $= 2 \times 10^{11}\text{ N/m}^2$ and Young's modulus of copper $= 1.5 \times 10^{11}\text{ N/m}^2$)

Two trucks A and B are approaching each other on a straight path with the velocities of $16\text{ m/s}$ and $20\text{ m/s}$ respectively. When they are $200\text{ m}$ apart their drivers see each other and applies the breaks simultaneously. If the truck A decelerates with $2\text{ m/s}^2$ and truck B decelerates with $4\text{ m/s}^2$, what is the distance between them when they finally stop?

A wire of length $8\text{ m}$ is bent to form a circular loop in y-z plane. A current of $0.5\text{ A}$ is flowing in anticlockwise direction in it, the magnetic dipole moment of the loop is:

In the following loop, magnitude of the magnetic field produced at the centre (O) of the loop is: (Assume AB and CD are infinitely extended):

An oscillating simple pendulum of time period $T_0$ is placed in a lift which is accelerating upwards with $2.5\text{ m/s}^2$. The time period of pendulum in the lift will be (if $g = 10\text{ m/s}^2$)

A particle executing SHM has its velocity $20\text{ cm s}^{-1}$ at mean position and acceleration of $25\text{ cm s}^{-2}$ at one of its extreme position. The amplitude of the particle will be ____ cm.

Two projectiles are thrown towards each other at $15^\circ$ and $45^\circ$ angles respectively with the horizontal at the same speed. The difference between the horizontal distances traveled by the two projectiles is $80\text{ m}$. The initial speed of the projectiles is ______ $\text{m s}^{-1}$

[Given $g = 10\text{ m s}^{-2}$ ]

A ring is placed at the bottom of a trough containing four immiscible liquids of refractive indices $1.0, 2.0, 3.0$ and $4.0$ poured one above the other of heights $10\text{ cm}, 20\text{ cm}, 30\text{ cm}$, and $40\text{ cm}$ respectively. The apparent depth at which the ring appears, when seen from outside is __________ cm.

A fly wheel of mass $10\text{ kg}$ and radius $50\text{ cm}$ is rotating at a rate of $360$ rpm. Assuming mass to be concentrated at the rim, the constant retarding torque required to stop the rotation of wheel in $6$ rotations will be $x\pi\text{ N m}$. The value of $x$ is ________

The I-V characteristics given in above figure is related to:

A water drop of radius $1\text{ cm}$ is broken into eight equal droplets. Surface tension of water is $0.075\text{ N m}^{-1}$. The gain in surface energy is ___________ $\times 10^{-7}\text{ J}$. (Take $\pi = 3.14$)

A Carnot engine is operating between the two reservoirs of temperature $227^\circ\text{C}$ and $127^\circ\text{C}$ respectively. If the engine performs $1.04 \times 10^{5}\text{ J}$ work per cycle. Then, the heat absorbed from hot reservoir per cycle will be:

If current (I), kinetic energy (K) and charge (Q) are taken as the fundamental quantities, The dimensional representation of power will be:

Two poloroids $P_1$ and $P_2$ are placed parallel to each other with common axis.The light of intensity $I_0$ passes through a polaroid sheet $P_1$ and then passes through polaroid $P_2$. If $P_2$ is now rotated by $60^\circ$, then the intensity of the output light from $P_2$ will be: