JEE Main 2019 Physics Paper: 10 Apr, Shift 2

A coil of self inductance 10 mH and resistance 0.1 $\Omega$ is connected through a switch to a battery of internal resistance 0.9 $\Omega$. After the switch is closed, the time taken for the current to attain 80% of the saturation value is: [take ln 5 = 1.6]

In Li+ +, electron in first Bohr orbit is excited to a level by a radiation of wavelength $\lambda$. When the ion gets deexcited to the ground state in all possible ways (including intermediate emissions), a total of six spectral lines are observed. What is the value of $\lambda$?

(Given: H = 6.63 × 10–34 Js; c = 3 × 108 ms –1)

A simple pendulum of length L is placed between the plates of a parallel plate capacitor having electric field E, as shown in figure. Its bob has mass m and charge q. The time period of the pendulum is given by:

Space between two concentric conducting spheres of radii a and b (b > a) is filled with a medium of resistivity $\rho$. The resistance between the two spheres will be:

A 2 mW laser operates at wavelength of 500 nm. The number of photons that will be emitted per second is: [Given Planck's constant h = 6.6 × 10–34 Js, speed of light c = 3.0 × 108 m/s]

Light is incident normally on a completely absorbing surface with an energy flux of 25 W cm–2. If the surface has an area of 25 cm2, the momentum transferred to the surface in 40 min time duration will be:

In free space, a particle A of charge 1$\mu$C is held fixed at a point P. Another particle B of the same charge and mass 4$\mu$g is kept at a distance of 1 mm from P. If B is released, then its velocity at a distance of 9 mm from P is: $\left[\text{Take } \frac{1}{4\pi\epsilon_0} = 9 \times 10^{9}\text{ Nm}^2\text{C}^{-2}\right]$

Water from a tap emerges vertically downwards with an initial speed of 1.0 ms–1. The cross- sectional area of the tap is 10–4 m2. Assume that the pressure is constant throughout the stream of water and that the flow is streamlined. The cross-sectional area of the stream, 0.15 m below the tap would be: (Take g = 10 ms–2)

A cubical block of side 0.5 m floats on water with 30% of its volume under water. What is the maximum weight that can be put on the block without fully submerging it under water? [Take, density of water = 103 kg/m3]

A submarine experiences a pressure of 5.05 × 106 Pa at a depth of d1 in a sea. When it goes further to a depth of d2, it experiences a pressure of 8.08 × 106 Pa. Then d2 –d1 is approximately (density of water = 103 kg/m3 and acceleration due to gravity = 10 ms–2):

A spaceship orbits around a planet at a height of 20 km from its surface. Assuming that only gravitational field of the planet acts on the spaceship, what will be the number of complete revolutions made by the spaceship in 24 hours around the planet?

[Given; Mass of planet = 8 × 1022 kg, Radius of planet = 2 × 106 m, Gravitational constant G = 6.67 × 10–11 Nm2 /kg2]

A bullet of mass 20 g has an initial speed of 1 ms–1, just before it starts penetrating a mud wall of thickness 20 cm. If the wall offers a mean resistance of 2.5 × 10–2 N, the speed of the bullet after emerging from the other side of the wall is close to:

Two blocks A and B of masses mA = 1 kg and mB = 3 kg are kept on the table as shown in figure. The coefficient of friction between A and B is 0.2 and between B and the surface of the table is also 0.2. The maximum force F that can be applied on B horizontally, so that the block A does not slide over the block B is:

[Take g = 10 m/s2]

The elastic limit of brass is 379 MPa. What should be the minimum diameter of a brass rod if it is to support a 400 N load without exceeding its elastic limit?

In an experiment, brass and steel wires of length 1 m each with areas of cross section 1mm2 are used. The wires are connected in series and one end of the combined wire is connected to a rigid support and other end is subjected to elongation. The stress required to produce a net elongation of 0.2 mm is, [Given, the Young's Modulus for steel and brass are, respectively, 120 × 109 N/m2 and 60 × 109 N/m2]

A square loop is carrying a steady current I and the magnitude of its magnetic dipole moment is m. if this square loop is changed to a circular loop and it carries the same current, the magnitude of the magnetic dipole moment of circular loop will be:

The magnitude of the magnetic field at the centre of an equilateral triangular loop of side 1 m which is carrying a current of 10 A is:

[Take $\mu$0 = 4$\pi$ × 10–7 NA–2]

Two radioactive substances A and B have decay constants 5$\lambda$ and $\lambda$ respectively. At t = 0, a sample has the same number of the two nuclei. The time taken for the ratio of the number of nuclei to become $\left(\frac{1}{e}\right)^2$ will be:

A plane is inclined at an angle $\alpha$ = 30° with respect to the horizontal. A particle is projected with a speed u = 2 ms–1, from the base of the plane, making an angle $\theta$ = 15° with respect to the plane as shown in the figure. The distance from the base, at which the particle hits the plane is close to: (Take g = 10 ms–2)

The graph shows how the magnification m produced by a thin lens varies with image distance v. What is the focal length of the lens used?

The time dependence of the position of a particle of mass m = 2 is given by$\vec{r}(t) = 2t\hat{i} - 3t^{2}\hat{j}$. Its angular momentum, with respect to the origin, at time t = 2 is

A solid sphere of mass M and radius R is divided into two unequal parts. The first part has a mass of $\frac{7M}{8}$ and is converted into a uniform disc of radius 2R. The second part is converted into a uniform solid sphere. Let I1 be the moment of inertia of the disc about its axis and I2 be the moment of inertia of the new sphere about its axis. The ratio I1/I2 is given by:

A metal coin of mass 5 g and radius 1 cm is fixed to a thin stick AB of negligible mass as shown in the figure. The system is initially at rest. The constant torque, that will make the system rotate about AB at 25 rotations per second in 5s, is close to:

The figure represents a voltage regulator circuit using a Zener diode. The breakdown voltage of the Zener diode is 6 V and the load resistance is, RL = 4k$\Omega$. The series resistance of the circuit is Ri = 1 k$\Omega$. If the battery voltage VB varies from 8 V to 16 V, what are the minimum and maximum values of the current through Zener diode?

When heat Q is supplied to a diatomic gas of rigid molecules, at constant volume its temperature increases by $\Delta$T. the heat required to produce the same change in temperature, at a constant pressure is:

One mole of ideal gas passes through a process where pressure and volume obey the relation ${}$

$P = P_0\left[1 - \frac{1}{2}\left(\frac{V_0}{V}\right)^{2}\right]$. Here P0 and V0 are constants. Calculate the change in the temperature of the gas if its volume changes form V0 to 2V0

In the formula X = 5YZ2, X and Z have dimensions of capacitance and magnetic field, respectively. What are the dimensions of Y in SI units?

The correct figure that shows, schematically, the wave pattern produced by superposition of two waves of frequencies 9 Hz and 11 Hz, is:

A source of sound S is moving with a velocity of 50 m/s towards a stationary observer. The observer measures the frequency of the source as 1000 Hz. What will be the apparent frequency of the source when it is moving away from the observer after crossing him? (Take velocity of sound in air is 350 m/s)

In a Young's double slit experiment, the ratio of the slit's width is 4: 1. The ratio of the intensity of maxima to minima, close to the central fringe on the screen, will be: