JEE Main 2020 Physics Paper: 5 Sep, Shift 1

A particle of mass 200 MeV/c2 collides with a hydrogen atom at rest. Soon after the collision the particle comes to rest, and the atom recoils and goes to its first excited state. The initial kinetic energy of the particle (in eV) is

$\frac{N}{4}$. The value of N is:

(Given the mass of the hydrogen atom to be 1 GeV/c2) ______.

Two capacitors of capacitances C and 2C are charged to potential differences V and 2V, respectively. These are then connected in parallel in such a manner that the positive terminal of one is connected to the negative terminal of the other. The final energy of this configuration is:

An electrical power line, having a total resistance of 2 $\Omega$, delivers 1 kW at 220 V. The efficiency of the transmission line is approximately:

A galvanometer of resistance G is converted into a voltmeter of range 0 – 1 V by connecting a resistance R1 in series with it. The additional resistance that should be connected in series with R1 to increase the range of the voltmeter to 0 – 2 V will be:

A beam of electrons of energy E scatters from a target having atomic spacing of 1 $\text{\AA}$. The first maximum intensity occurs at $\theta$ = 60o. Then E (in eV) is ______.

(Planck constant h = 6.64 × 10–34 Js,

1 eV = 1.6 × 10–19 J, electron

mass m = 9.1 × 10–31 kg)

Two concentric circular coils, C1 and C2 are

placed in the XY plane. C1 has 500 turns, and

a radius of 1 cm. C2 has 200 turns and radius

of 20 cm. C2 carries a time dependent current

I(t) = (5t2 – 2t + 3) A where t is in s. The emf

induced in C1 (in mV), at the instant t = 1 s is

$\frac{4}{x}$. The value of x is ___.

An electron is constrained to move along the y-axis with a speed of 0.1 c (c is the speed of light) in the presence of electromagnetic wave, whose electric field is

$\vec{E} = 30\hat{j} \sin\left(1.5 \times 10^{7} t - 5 \times 10^{-2} x\right)$ V/m.

The maximum magnetic force experienced by the electron will be:

(given c = 3 $\times$ 108 ms–1 and electron charge = 1.6 $\times$ 10–19 C)

A solid sphere of radius R carries a charge Q + q distributed uniformly over its volume. A very small point like piece of it of mass m gets detached from the bottom of the sphere and falls down vertically under gravity. This piece carries charge q. If it acquires a speed v when it has fallen through a vertical height y (see figure), then:

(assume the remaining portion to be spherical).

A hollow spherical shell of outer radius R floats just submerged under the water surface. The inner radius of the shell is r. If the specific gravity of the shell material is $\frac{27}{8}$ w.r.t water, the value of r is:

The value of the acceleration due to gravity is g1 at a height h = $\frac{R}{2}$ (R = radius of the earth) from the surface of the earth. It is again equal to g1 at a depth d below the surface of the earth. The ratio $\left(\frac{d}{R}\right)$ equals:

Number of molecules in a volume of 4 cm3 of a perfect monoatomic gas at some temperature T and at a pressure of 2 cm of mercury is close to?

(Given, mean kinetic energy of a molecule

(at T) is 4 $\times$ 10–14 erg, g = 980 cm/s2, density of

mercury = 13.6 g/cm3)

A helicopter rises from rest on the ground vertically upwards with a constant acceleration g. A food packet is dropped from the helicopter when it is at a height h. The time taken by the packet to reach the ground is close to:

[g is the acceleration due to gravity]

______

A square loop of side 2$a$, and carrying current I, is kept in XZ plane with its centre at origin. A long wire carrying the same current I is placed parallel to the z-axis and passing through the point (0, b, 0), (b >> a). The magnitude of the torque on the loop about z-axis is given by:

Activities of three radioactive substances A, B and C are represented by the curves A, B and C, in the figure. Then their half-lives

$T_{\frac{1}{2}}(A)$: $T_{\frac{1}{2}}(B)$: $T_{\frac{1}{2}}(C)$ are in the ratio:

A balloon is moving up in air vertically above a point A on the ground. When it is at a height h1, a girl standing at a distance d (point B) from A (see figure) sees it at an angle 45o with respect to the vertical. When the balloon climbs up a further height h2, it is seen at an angle 60o with respect to the vertical if the girl moves further by a distance 2.464 d (point C). Then the height h2 is (given tan 30o = 0.5774)

A compound microscope consists of an objective lens of focal length 1 cm and an eyepiece of focal length 5 cm with a separation of 10 cm.

The distance between an object and the objective lens, at which the strain on the eye is minimum is $\frac{n}{40}$ cm. The value of n is _____.

For a concave lens of focal length f, the relation between object and image distances u and v, respectively, from its pole can best be represented by (u = v is the reference line):

A wheel is rotating freely with an angular speed $\omega$ on a shaft. The moment of inertia of the wheel is I and the moment of inertia of the shaft is negligible. Another wheel of moment of inertia 3I initially at rest is suddenly coupled to the same shaft. The resultant fractional loss in the kinetic energy of the system is:

A force $\vec{F} = \left(\hat{i} + 2\hat{j} + 3\hat{k}\right)$ N acts at a point

$\left(4\hat{i} + 3\hat{j} - \hat{k}\right)$ m. Then the magnitude of torque

about the point $\left(\hat{i} + 2\hat{j} + \hat{k}\right)$ m will be $\sqrt{x}$ N m.

The value of x is _______.

With increasing biasing voltage of a photodiode, the photocurrent magnitude:

Three different processes that can occur in an ideal monoatomic gas are shown in the P vs V diagram. The paths are labelled as A $\rightarrow$ B, A $\rightarrow$ C and A $\rightarrow$ D. The change in internal energies during these process are taken as EAB, EAC and EAD and the work done as WAB, WAC and WAD. The correct relation between these parameters are:

A bullet of mass 5 g, travelling with a speed of 210 m/s, strikes a fixed wooden target. One half of its kinetic energy is converted into heat in the bullet while the other half is converted into heat in the wood. The rise of temperature of the bullet if the specific heat of its material is 0.030 cal/(g –oC) (1 cal = 4.2 × 107 ergs) close to:

A physical quantity z depends on four observables

a, b, c and d, as z = $\frac{a^{2} b^{\frac{2}{3}}}{\sqrt{c}\, d^{3}}$. The percentages of error in the measurement of a, b, c and d are 2%, 1.5%, 4% and 2.5% respectively. The percentage of error in z is:

In a resonance tube experiment when the tube is filled with water up to a height of 17.0 cm from bottom, it resonates with a given tuning fork. When the water level is raised the next resonance with the same tuning fork occurs at a height of 24.5 cm. If the velocity of sound in air is 330 m/s, the tuning fork frequency is:

Assume that the displacement(s) of air is proportional to the pressure difference ($\Delta$p) created by a sound wave. Displacement (s) further depends on the speed of sound (v), density of air ($\rho$) and the frequency (f). If $\Delta$p ~ 10 Pa, v ~ 300 m/s, $\rho$ ~ 1 kg/m3 and f ~ 1000 Hz, then s will be of the order of (take the multiplicative constant to be 1):