JEE MAIN - Physics (2020 - 9th January Morning Slot)

1
In a fluorescent lamp choke (a small transformer) 100 V of reverse voltage is produced when the choke current changes uniformly from 0.25 A to 0 in a duration of 0.025 ms. The self-inductance of the choke (in mH) is estimated to be ________.
پاسخ دهید
10
2
Both the diodes used in the circuit shown are assumed to be ideal and have negligible resistance when these are forward biased. Built in potential in each diode is 0.7 V. For the input voltages shown in the figure, the voltage (in Volts) at point A is __________.
پاسخ دهید
12
3
A body of mass m = 10 kg is attached to one end of a wire of length 0.3 m. The maximum angular speed (in rad s^–1) with which it can be rotated about its other end in space station is :
(Breaking stress of wire = 4.8 × 10⁷ Nm^–2 and
area of cross-section of the wire = 10^–2 cm²) is:
پاسخ دهید
4
4
The distance x covered by a particle in one dimensional motion varies with time t as
x² = at² + 2bt + c. If the acceleration of the particle depends on x as x^–n, where n is an integer, the value of n is __________
پاسخ دهید
3
5
One end of a straight uniform 1m long bar is pivoted on horizontal table. It is released from rest when it makes an angle 30º from the horizontal (see figure). Its angular speed when it hits the table is given as $$\sqrt n $$ s^-1, where n is an integer. The value of n is _________.
پاسخ دهید
15
6
Water flows in a horizontal tube (see figure).
The pressure of water changes by 700 Nm^–2
between A and B where the area of cross section
are 40 cm² and 20 cm², respectively. Find the
rate of flow of water through the tube.
(density of water = 1000 kgm^–3)
پاسخ دهید
(D)
2720 cm³/s
7
Three solid spheres each of mass m and diameter d are stuck together such that the lines connecting the centres form an equilateral triangle of side of length d. The ratio I₀/I_A of moment of inertia I₀ of the system about an axis passing the centroid and about center of any of the spheres I_A and perpendicular to the plane of the triangle is :
پاسخ دهید
(A)
$${{13} \over {23}}$$
8
An electric dipole of moment
$$\overrightarrow p = \left( { - \widehat i - 3\widehat j + 2\widehat k} \right) \times {10^{ - 29}} $$ C.m is
at the origin (0, 0, 0). The electric field due to this dipole at
$$\overrightarrow r = + \widehat i + 3\widehat j + 5\widehat k$$ (note that $$\overrightarrow r .\overrightarrow p = 0$$ ) is parallel to :
پاسخ دهید
(A)
$$\left( { + \widehat i + 3\widehat j - 2\widehat k} \right)$$
9
Three harmonic waves having equal frequency $$\nu $$ and same intensity $${I_0}$$, have phase angles 0, $${\pi \over 4}$$ and $$ - {\pi \over 4}$$ respectively. When they are superimposed the intensity of the resultant wave is close to :
پاسخ دهید
(A)
5.8 I₀
10
A charged particle of mass 'm' and charge 'q' moving under the influence of uniform electric field $$E\overrightarrow i $$ and a uniform magnetic field $$B\overrightarrow k $$ follows a trajectory from point P to Q as shown in figure. The velocities at P and Q are respectively, $$v\overrightarrow i $$ and $$ - 2v\overrightarrow j $$ . Then which of the following statements (A, B, C, D) are the correct ?
(Trajectory shown is schematic and not to scale) :
(A) E = $${3 \over 4}\left( {{{m{v^2}} \over {qa}}} \right)$$

(B) Rate of work done by the electric field at P is $${3 \over 4}\left( {{{m{v^3}} \over a}} \right)$$

(C) Rate of work done by both the fields at Q is zero

(D) The difference between the magnitude of angular momentum of the particle at P and Q is 2mav.
پاسخ دهید
(B)
(A), (B), (C)
11
Which of the following is an equivalent cyclic process corresponding to the thermodynamic cyclic given in the figure ? where, 1 $$ \to $$ 2 is adiabatic.
(Graphs are schematic and are not to scale)
پاسخ دهید
(B)
12
In the given circuit diagram, a wire is joining points B and D. The current in this wire is :
پاسخ دهید
(B)
2 A
13
Two particles of equal mass m have respective
initial velocities $$u\widehat i$$ and $$u\left( {{{\widehat i + \widehat j} \over 2}} \right)$$.
They collide completely inelastically. The energy lost in the process is :
پاسخ دهید
(B)
$${1 \over 8}m{u^2}$$
14
If the screw on a screw-gauge is given six rotations, it moves by 3 mm on the main scale. If there are 50 divisions on the circular scale the least count of the screw gauge is :
پاسخ دهید
(D)
0.001 cm
15
Consider two ideal diatomic gases A and B at some temperature T. Molecules of the gas A are rigid, and have a mass m. Molecules of the gas B have an additional vibrational mode, and have a mass $${m \over 4}$$ . The ratio of the specific heats ($$C_V^A$$ and $$C_V^B$$ ) of gas A and B, respectively is :
پاسخ دهید
(B)
5 : 7
16
A particle moving with kinetic energy E has de Broglie wavelength $$\lambda $$. If energy $$\Delta $$E is added to its energy, the wavelength become $$\lambda $$/2. Value of $$\Delta $$E, is :
پاسخ دهید
(B)
3E
17
Consider a force $$\overrightarrow F = - x\widehat i + y\widehat j$$ . The work done by this force in moving a particle from point A(1, 0) to B(0, 1) along the line segment is : (all quantities are in SI units)
پاسخ دهید
(C)
1
18
A body A of mass m is moving in a circular orbit of radius R about a planet. Another body B of mass $${m \over 2}$$ collides with A with a velocity which is half $$\left( {{{\overrightarrow v } \over 2}} \right)$$ the instantaneous velocity$${\overrightarrow v }$$ of A. The collision is completely inelastic. Then, the combined body :
پاسخ دهید
(A)
starts moving in an elliptical orbit around the planet.
19
Consider a sphere of radius R which carries a uniform charge density $$\rho $$. If a sphere of radius $${{R \over 2}}$$ is carved out of it, as shown, the ratio $${{\left| {\overrightarrow {{E_A}} } \right|} \over {\left| {\overrightarrow {{E_B}} } \right|}}$$ of magnitude of electric field $${\overrightarrow {{E_A}} }$$ and $${\overrightarrow {{E_B}} }$$, respectively, at points A and B due to the remaining portion is :
پاسخ دهید
(C)
$${{18} \over {34}}$$
20
The electric fields of two plane electromagnetic plane waves in vacuum are given by
$$\overrightarrow {{E_1}} = {E_0}\widehat j\cos \left( {\omega t - kx} \right)$$ and
$$\overrightarrow {{E_2}} = {E_0}\widehat k\cos \left( {\omega t - ky} \right)$$
At t = 0, a particle of charge q is at origin with
a velocity $$\overrightarrow v = 0.8c\widehat j$$ (c is the speed of light in vacuum). The instantaneous force experienced by the particle is :
پاسخ دهید
(C)
$${E_0}q\left( {0.8\widehat i + \widehat j + 0.2\widehat k} \right)$$
21
A long, straight wire of radius a carries a current distributed uniformly over its cross-section. The ratio of the magnetic fields due to the wire at distance $${a \over 3}$$ and 2$$a$$, respectively from the axis of the wire is :
پاسخ دهید
(D)
$${2 \over 3}$$
22
Radiation, with wavelength 6561 $$\mathop A\limits^o $$ falls on a metal surface to produce photoelectrons. The electrons are made to enter a uniform magnetic field of 3 × 10^–4 T. If the radius of the largest circular path followed by the electrons is 10 mm, the work function of the metal is close to :
پاسخ دهید
(C)
1.1eV
23
The aperture diameter of a telescope is 5m. The separation between the moon and the earth is 4 × 10⁵ km. With light of wavelength of 5500 $$\mathop A\limits^o $$, the minimum separation between objects on the surface of moon, so that they are just resolved, is close to :
پاسخ دهید
(D)
60 m
24
A vessel of depth 2h is half filled with a liquid of refractive index $$2\sqrt 2 $$ and the upper half with another liquid of refractive index $$\sqrt 2 $$ . The liquids are immiscible. The apparent depth of the inner surface of the bottom of vessel will be :
پاسخ دهید
(C)
$${3 \over 4}h\sqrt 2 $$
25
A quantity f is given by $$f = \sqrt {{{h{c^5}} \over G}} $$ where c is speed of light, G universal gravitational constant and h is the Planck's constant. Dimension of f is that of :
پاسخ دهید
(A)
Energy