JEE Main 2022 Physics Paper: 25 Jul, Shift 2

When you walk through a metal detector carrying a metal object in your pocket, it raises an alarm. This phenomenon works on:

Hydrogen atom from excited state comes to the ground state by emitting a photon of wavelength $\lambda$. The value of principal quantum number '$n$' of the excited state will be: ($R:$ Rydberg constant)

$\frac{x}{x+4}$ is the ratio of energies of photons produced due to transition of an electron of hydrogen atom from its

(i) third permitted energy level to the second level and

(ii) the highest permitted energy level to the second permitted level.

The value of x will be ____________.

Capacitance of an isolated conducting sphere of radius R1 becomes n times when it is enclosed by a concentric conducting sphere of radius R2 connected to earth. The ratio of their radii $\left(\frac{R_2}{R_1}\right)$ is:

Two parallel plate capacitors of capacity C and 3C are connected in parallel combination and charged to a potential difference 18 V. The battery is then disconnected and the space between the plates of the capacitor of capacity C is completely filled with a material of dielectric constant 9. The final potential difference across the combination of capacitors will be ___________ V.

Three identical spheres each of mass M are placed at the corners of a right angled triangle with mutually perpendicular sides equal to 3 m each. Taking point of intersection of mutually perpendicular sides as origin, the magnitude of position vector of centre of mass of the system will be $\sqrt{x}$ m. The value of x is ____________.

A current of 15 mA flows in the circuit as shown in figure. The value of potential difference between the points A and B will be:

In a potentiometer arrangement, a cell of emf 1.20 V gives a balance point at 36 cm length of wire. This cell is now replaced by another cell of emf 1.80 V. The difference in balancing length of potentiometer wire in above conditions will be ___________ cm.

The ratio of wavelengths of proton and deuteron accelerated by potential Vp and Vd is 1: $\sqrt{2}$. Then the ratio of Vp to Vd will be:

Magnetic flux (in weber) in a closed circuit of resistance 20 $\Omega$ varies with time t(s) at $\phi$ = 8t2 $-$ 9t + 5. The magnitude of the induced current at t = 0.25 s will be ____________ mA.

Light wave travelling in air along x-direction is given by $E_y = 540\sin\pi\times 10^{4}(x - ct)\text{ V m}^{-1}$. Then, the peak value of magnetic field of wave will be (Given c = 3 $\times$ 108 ms${}^{-1}$)

The length of a seconds pendulum at a height h = 2R from earth surface will be: (Given R = Radius of earth and acceleration due to gravity at the surface of earth, g = $\pi$2 ms${}^{-2}$)

An object is taken to a height above the surface of earth at a distance $\frac{5}{4}$ R from the centre of the earth. Where radius of earth, R = 6400 km. The percentage decrease in the weight of the object will be:

Sound travels in a mixture of two moles of helium and n moles of hydrogen. If rms speed of gas molecules in the mixture is $\sqrt{2}$ times the speed of sound, then the value of n will be:

For a free body diagram shown in the figure, the four forces are applied in the 'x' and 'y' directions. What additional force must be applied and at what angle with positive x-axis so that the net acceleration of body is zero?

A particle is moving in a straight line such that its velocity is increasing at 5 ms${}^{-1}$ per meter. The acceleration of the particle is _____________ ms${}^{-2}$ at a point where its velocity is 20 ms${}^{-1}$.

The electric current in a circular coil of 2 turns produces a magnetic induction B1 at its centre. The coil is unwound and is rewound into a circular coil of 5 turns and the same current produces a magnetic induction B2 at its centre. The ratio of $\frac{B_2}{B_1}$ is

A ball is projected from the ground with a speed 15 ms${}^{-1}$ at an angle $\theta$ with horizontal so that its range and maximum height are equal,

then 'tan $\theta$' will be equal to:

A convex lens of focal length 20 cm is placed in front of a convex mirror with principal axis coinciding each other. The distance between the lens and mirror is 10 cm. A point object is placed on principal axis at a distance of 60 cm from the convex lens. The image formed by combination coincides the object itself. The focal length of the convex mirror is ____________ cm.

For an object placed at a distance 2.4 m from a lens, a sharp focused image is observed on a screen placed at a distance 12 cm from the lens. A glass plate of refractive index 1.5 and thickness 1 cm is introduced between lens and screen such that the glass plate plane faces parallel to the screen. By what distance should the object be shifted so that a sharp focused image is observed again on the screen?

Two ideal diodes are connected in the network as shown in figure. The equivalent resistance between A and B is __________ $\Omega$.

A drop of liquid of density $\rho$ is floating half immersed in a liquid of density $\sigma$ and surface tension $7.5 \times 10^{-4}$ Ncm${}^{-1}$. The radius of drop in $\text{cm}$ will be:

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

Let $\eta_1$ is the efficiency of an engine at $T_1 = 447^\circ\text{C}$ and $\mathrm{T}_2 = 147^\circ\text{C}$ while $\eta_2$ is the efficiency at $\mathrm{T}_1 = 947^\circ\text{C}$ and $\mathrm{T}_2 = 47^\circ\text{C}$. The ratio $\frac{\eta_1}{\eta_2}$ will be:

A block of ice of mass 120 g at temperature 0$^{\circ}$C is put in 300 g of water at 25$^{\circ}$ C. The x g of ice melts as the temperature of the water reaches 0$^{\circ}$ C. The value of x is _____________. [Use specific heat capacity of water = 4200 Jkg$^{-1}\text{K}^{-}$1, Latent heat of ice = 3.5 $\times$ 105 Jkg$^{-}$1]

The maximum error in the measurement of resistance, current and time for which current flows in an electrical circuit are $1\%,\ 2\%$ and $3\%$ respectively. The maximum percentage error in the detection of the dissipated heat will be:

Two waves executing simple harmonic motions travelling in the same direction with same amplitude and frequency are superimposed. The resultant amplitude is equal to the $\sqrt{3}$ times of amplitude of individual motions. The phase difference between the two motions is ___________ (degree).

A bag of sand of mass 9.8 kg is suspended by a rope. A bullet of 200 g travelling with speed 10 ms${}^{-1}$ gets embedded in it, then loss of kinetic energy will be: