1. REST AND MOTION :
* An object is said to be in motion wrt a frame of reference S_{1}, when its location is changing with time in same frame of reference S_{1}.
* Rest and motion are relative terms.
]]>1. REST AND MOTION :
* An object is said to be in motion wrt a frame of reference S_{1}, when its location is changing with time in same frame of reference S_{1}.
* Rest and motion are relative terms.
* Absolute rest and absolute motion have no meaning.
Motion is broadly classified into 3 categories.
1. Rectilinear and translatory motion.
2. Circular and rotatory motion.
3. Oscillatory and vibratory motion.
1.1 Rectilinear or 1-D Motion
When a particle is moving along a straight line, then its motion is a rectilinear motion.
Parameters of rectilinear motion or translatory motion or plane motion:
(A) Time :
* It is a scalar quantity and its SI unit is second(s).
* At a particular instant of time, a physical object can be present at one location only.
* Time can never decrease.
(B) Position or location - It is defined with respect to some reference point (origin) of given frame of reference.
Consider a particle which moves from location
(at time t_{1})
to location
(at time t_{2}) as shown in the figure below, following path ACB.
]]>Dear students & parents, as the time for the final exam, is nearing, every student is busy in the last minute preparation (or) revision. During these slag hours, it is also important to focus on Non-academic alerts apart from regular last-minute tips. This includes, what to carry to the exam hall, reporting timings, exam hall behavior, do’s & don’ts, which are quint-essential to avoid last-minute haste.
Downloaded admit card with proper details of the student such as
(i) Name
(ii) Date of Birth
(iii) Paper
(iv) Gender
(v) Test center/city & state
(vi) Reservation category.
If a student finds any information incorrect, contact NTA immediately over the phone. The help-line numbers are displayed in Jee(main) official website
www.jeemain.nic.in
One passport size photograph, which is the same as uploaded in the online JEE(Main) application form, (will be pasted on the attendance sheet at the exam center.)
Original photo identity card (any of these) issued by the [Government (State or Central)]
(i) Aadhar card (or E-aadhar)
(ii) Driving license
(iii) Voter ID
(iv) Passport
If a body moves to and fro about a mean position repeatedly, then that motion is called oscillatory motion. Periodic motion is a motion that repeats itself after a fixed interval of time. It is not necessary that in periodic motion the body moves in to and fro motion.
Oscillatory motion is always periodic but vice-versa is not true. For example: motion of wheel of car is only periodic because it moves in a circular motion. Examples of oscillatory motion are: oscillations of simple pendulum, vibrations of the mass attached to a string etc.
As we know Periodic motion is a motion that repeats itself after a fixed interval of time. So, the shortest time taken by an object to repeat its motion is called Time Period of that motion represented by ‘T’.
The reciprocal of the time period tells us the number of repetitions of the motion in a unit time. It is called Frequency of the periodic motion represented by ‘v’. The unit of frequency is hertz:
$\mathrm{V}=1 / \mathrm{T}$
Now consider a block attached to a spring on one end. The other end of spring is fixed to a wall. Now suppose the surface is frictionless then the motion of the block can be described in terms of displacement ‘x’ of the wall.
Similarly, in a pendulum the motion can be described in terms of the angle of the string from the wall which is called angular displacement from the vertical.
A function that repeats its value on regular interval or periods is called a periodic function. In the graph of a periodic function we can observe that a single pattern is being repeated over and over again. Example: trigonometric functions etc.
The simplest periodic function can be written as:
$\mathrm{F}(\mathrm{t})=\mathrm{A} \cos (\omega \mathrm{t})$
When the restoring force is directly proportional to the displacement from equilibrium, the resulting periodic motion is called simple harmonic motion (SHM). The object in a harmonic motion moves in a uniform path with a variable force acting on it. The magnitude of force is proportional to the displacement of the mass and the force is always opposite in direction to the displacement direction.
If a particle is oscillating along the y-axis, its location on the y-axis at any given instant of time t, measured from the start of the oscillation is given by the equation
$y=A \sin (2 \pi f t)$
now as we know velocity is the first derivative of displacement thus velocity at time t is,
$v=2 \pi f A \underbrace{\cos (2 \pi f t)}$
and acceleration is second derivative of the displacement hence at time t it is equal to,
$a=-(2 \pi f) 2[A \underline{\sin (2 \pi f t)}]$
Here we will notice that both velocity and acceleration are also sinusoidal. But velocity has a $90^{\circ}$ or $\pi / 2$ phase difference while the acceleration function has a $180^{\circ}$ or $\pi$ phase difference relative to the displacement function.
This means that if displacement is positive max. then the velocity is zero and the acceleration is negative maximum.
In a block and spring example there is a force acting on the block that tries to return the block to its equilibrium position. This force is the restoring force and the force law for simple harmonic motion is based on this force. Let the displacement of the block from its equilibrium position be x and the restoring force be F.
We know restoring force is directly proportional to displacement but in opposite direction hence,
$F=-k x$
here k is a constant known as the force constant and its unit is N/m in S.I. system.
Now we can also substitute in equation $(1), \mathrm{a}=\mathrm{F} / \mathrm{m}$ and we will get:
$a=-k x / m=-\omega^{2} \underline{x}\left(\text {where } k / m=\omega^{2}\right)$
So, equation (1) and (2) give us the force laws of the simple harmonic motion.
Suppose there is a pendulum, at its extreme position it is at rest so it only possesses potential energy and at the lowest point it has max speed with max kinetic energy.
Hence energy of simple harmonic motion can be calculated by combining both potential as well as kinetic.
As we know kinetic energy is energy dur to motion. The instantaneous velocity of the particle performing S.H.M. at a distance x from the mean position is given by
$v^{2}=\omega^{2}\left(\underline{a}^{2}-x^{2}\right)$. Hence,
Kinetic energy
$=\frac{1}{2} m v^{2}=\frac{1}{2} m \omega^{2}\left(a^{2}=x^{2}\right)$
Similarly, energy possessed due to position is potential energy. You know the restoring force acting on the particle at a displacement x is $\mathrm{F}=-\mathrm{kx}$ where k is the force constant.
Now, the particle is given further infinitesimal displacement dx against the restoring force F. Let the work done to displace the particle be dW. Therefore, the work done dW during the displacement is
$d W=-f d x=-(-k x) d x=k x d x$
Therefore, the total work done to displace the particle now from 0 to x is
$\int d W=\int k x d x=k \int X d X$
Hence Total work done $=\frac{1}{2} \mathrm{kx}^{2}=\frac{1}{2} \mathrm{m} \omega^{2} \mathrm{x}^{2}$
The total work done here is stored in the form of potential energy.
So, this gives us the total energy of simple harmonic motion at any point. The sum of both the energies gives us the total energy of the simple harmonic motion.
Hence, $\mathrm{T.E.}=\mathrm{E}=\frac{1}{2} \mathrm{m\omega}^{2} \mathrm{a}^{2}$
The law of conservation of energy states that energy can neither be created nor destroyed. Therefore, the total energy in simple harmonic motion will always be constant. However, kinetic energy and potential energy are interchangeable.
When an external force acts on the motion of an oscillator its motion gets damped. So, these periodic motions with amplitude decreasing gradually is known as damped harmonic motion. Generally, the forces that are the reason of damping are frictional forces.
Damping force is directly proportional to velocity of object and acts in the opposite direction of velocity. It depends on the surroundings and medium. If the damping force is $F_{d}$, we have,
$F_{d}=-b v(\mathrm{I})$
where the constant b depends on the properties of the medium (viscosity, for example) and size and shape of the block.
The expression of damped harmonic motion is given by equation as:
$m\left(d^{R} x / d t^{2}\right)+b(d x / d t)+k x=0$
Now we can obtain expression of position and energy at any time in a damped motion by solving equation (1).
The expression for the position is,
$x(t)=A e_{w}^{-b t / 2 m} \cos (\omega t+\varnothing)$
where A is the amplitude and $\omega$ is the angular frequency of damped simple harmonic motion given by,
$\omega=\underline{V}\left(K / m-b^{2} / 4 m^{2}\right)$
and similarly, energy expression of the same would be given by,
$E(t)=1 / 2 k A e^{-b t / 2 m}$
if we displace the pendulum by a very small angle $\Theta$, then it performs the simple harmonic motion.
As gravity points down, we need to take the component of gravity which is parallel to its motion. Only the component of gravity which is parallel to the direction of motion will do work. In this case, the force on a pendulum can be given as
$F=m g \sin \theta$
Now let $\sin \theta=\theta$ be the assumption for very small $\theta$ the we will get,
$F=-m g \theta=-m g x / L$
So, we can say that for small displacement the simple pendulum performs simple harmonic motion.
Now time period of the simple pendulum is given by,
$T=2 \pi / \omega=2 \pi /$ Vacceleration per unit displacement
And acceleration per unit displacement $=a / x=g / L$
Hence the formula becomes,
$T=2 \pi / \sqrt{g} / L=2 \pi \sqrt{L / g}$
Similarly, the frequency of a simple pendulum is given by,
$f=1 / T=1 / 2 \pi \sqrt{g} / L$
In the previous section we read about damping motion. Now if we apply some external force so that the damping force cancels out and the object keeps on oscillating. The motion that the system performs under this external agency is known as Forced Simple Harmonic Motion. The external force is itself periodic with a frequency ω_{d} which is known as the drive frequency.
Suppose the force applied to damped oscillator is given by,
$F(t)=F_{0} \cos \omega_{d} t$
Now as we know acceleration is second derivative of displacement thus the damping equations modifies to,
$m\left(d^{2} x / d t^{2}\right)+b(d x / d t)+k x=F_{0} \cos \omega_{d} t$
the equation of an oscillator of mass m on which a periodic force of frequency $\omega_{d}$_{ }is applied.
The phenomenon of driving a system with a frequency equal to its natural frequency is called resonance. As the driving frequency gets progressively higher than the resonant or natural frequency, the amplitude of the oscillations becomes smaller, until the oscillations nearly disappear
The following graph shows the resonant frequency and different shapes for different type of damped oscillations.
At first, we study about oscillations and then we distinguished between oscillatory and periodic motion. Then we study about different quantities like time period, frequency ad displacement of a periodic motion. One of the most important periodic motion is simple harmonic motion. The chapter tells you about the velocity and acceleration of an object under SHM and also talks about its energy. Then we discuss about the spring mass system and Hooke’s law. We get to know that simple pendulum also undergoes SHM. This all was going on when there were no external forces by the surroundings. Then we talked about damping and to overcome damping we got to know about forced oscillations and resonance.
This blog lays down the important concepts associated with Atoms and gives the students insights of its application for problem solving.
Atoms are the most fundamental unit of matter. Molecules are combinations of atoms of different atoms in different proportions. Atoms play an important role in determining the nature of a substance. Atoms are composed of electrons, protons and neutrons, of which protons and neutrons reside inside the nucleus and electrons revolve around the nucleus in orbits.
An alpha particle is identical to a helium atom that has been stripped of its two electrons; thus, an alpha particle contains two protons and two neutrons. Because an alpha particle has no electrons to balance the positive charge of the two protons, it has a charge of +2 and can be represented as He2+. If a particle has a charge, whether negative or positive, it can be shown as a superscript. Thus He2+ means a helium atom that has lost two electrons and has a +2 charge. The symbol O2- means an oxygen atom that has added two electrons and thus has a charge of -2. Atoms that have acquired a charge by losing or gaining electrons are called ions.
Rutherford performed an experiment in which he bombarded a gold foil with alpha particles. It was observed that many alpha particles passed through the gold foil without any deviation and some were deviated and very few didn’t pass the gold foil and it seemed as if they collided with a heavy mass. From this Rutherford concluded that most part of the atom is empty and nearly all the mass of the atom is concentrated in the central part of the atom known as nucleus.
When electrons in an atom are excited by energy then they jump to higher energy levels where they are unstable, then to attain stability they jump back to their original energy level and in the process, they emit spectral lines of different wavelength. There are five spectral series observed in Hydrogen and Hydrogen like atoms, namely Balmer, Lyman, Paschen, Brackett and Pfund series. The wavelength of the Series is given by:
$\frac{1}{\lambda}=R\left(\frac{1}{n_{0}^{2}}-\frac{1}{n^{2}}\right)$,
Where n0 = 2, 3, 4, 5, 1 for Balmer, Paschen, Brackett, Pfund and Lyman series.
According to Bohr’s model of Hydrogen atom:
An electron revolves around the nucleus in orbits.
The angular momentum of the electron revolving in an orbit is $\mathrm{L}=\frac{n h}{2}$.
When an electron transits from a higher energy to a lower energy orbit then the extra energy gets radiated in the form of photon $h v=E_{i}-E_{f}$
The concept of atomic spectra applies to hydrogen atom as well, there are five spectral series observed in Hydrogen and Hydrogen like atoms, namely Balmer, Lyman, Paschen, Brackett and Pfund series. The wavelength of the Series is given by:
$\frac{1}{\lambda}=R\left(\frac{1}{n_{0}^{2}}-\frac{1}{n^{2}}\right)$,
Where n0 = 2, 3, 4, 5, 1 for Balmer, Paschen, Brackett, Pfund and Lyman series.
De-Broglie assumed that the wavelength associated with an electron must be an integral multiple of the circumference of the circular orbit, i.e. $2 \square r=r$. Now De-Broglie wavelength is given by $=\frac{h}{p}$. Therefore $2 \square r=n \frac{h}{p}$ , we know that p = mv, then on rearranging the above equation we get $\mathrm{mvr}=\frac{n h}{2 \pi}$.
Wavelength of spectral lines $\frac{1}{\lambda}=R\left(\frac{1}{n_{0}^{2}}-\frac{1}{n^{2}}\right)$,
Angular momentum of an electron in the nth orbit $\mathrm{L}=\frac{n h}{2}$.
Change in energy when an electron jumps from one energy level to another energy level,$h v=E_{i}-E_{f}$
In this blog we have seen what is an atom and its various constituents and how are ions formed from atoms. We have now studied the Rutherford’s experiment and its result, about the atomic spectra and the bohr model of hydrogen atom and de broglie's explanation of postulate of quantisation.
This blog lays down the important concepts associated with Dual Nature of Radiation and Matter and gives the students insights of its application for problem solving.
The Dual Nature of Radiation and Matter also known as the wave particle duality states that every particle has a wave nature and particle nature associated with it. The most common example is light it exhibits the wave nature of light in the Young’s Double slit Experiment and particle nature in photoelectric Experiment.
The phenomenon of escaping of electrons from the metal surface is known as electron emission. Electrons can be emitted from the metal surface with the help of heat energy, electric field or light wave.
When a light wave greater than or equal to a certain frequency strikes a certain metal surface then electrons escape from the surface of that metal, this is known as electron emission. The minimum frequency light wave which needs to be applied to emit electrons from the metal surface is known as the threshold frequency of the metal.
In this experiment the light waves were made incident on a metal plate inside a vacuum tube and the electrons emitted from that plate were collected at the plate at the other end of the tube. The two plates are connected to a power supply so that the emitter plate is negatively charged and the collector plate is positively charged. It was observed that when the intensity of light falling on the plate was increased then the number of electrons emitted from the metal surface increased. It was also observed that increasing the frequency of the incident light resulted in the increase of the energy of electrons emitted from the metal surface. The energy required to stop the emission of electrons for a particular frequency of light is known as the stopping potential of the metal for that particular frequency.
The photoelectric effect depicts the particle nature of light and the wave theory of light depicts the wave nature of light. In the photoelectric effect the light wave is considered to be a wave of photons and in wave theory light is considered a De-Broglie wave.
According to Einstein, the energy carried by each photon is given by:
E = h𝝂.
The energy of a photon goes into emitting the electron and the kinetic energy of the electron. Mathematically,
E = W + K.E.
Light wave is considered to be a stream of photons which are particles. Photons are discrete energy packets known as Quanta. Photons are electrically neutral. The energy of a photon is given by E = h𝝂. It is a massless particle.
As we have discussed above that light has a dual nature, i.e. wave nature as well as particle nature but what about matter does it only have particle nature. The answer is no matter also has a wave nature as particle nature. Now the question arises how do we know that matter has a wave associated with it. We can prove it using the mass energy equivalence relation of the Einstein’s equation $E=m c^{2}$ and Einstein Planck relation E = h𝝂. When we equate the two equations for a particle we get $\lambda=\frac{h}{p}$, where p is the momentum of the particle. This relation is known as the De Broglie relation.
The basic thought behind the Davisson and Germer experiment was that the waves reflected from two different atomic layers of a Ni crystal will have a fixed phase difference. After reflection, these waves will interfere either constructively or destructively.
Hence producing a diffraction pattern. In the Davisson and Germer experiment waves were used in place of electrons. These electrons formed a diffraction pattern. The dual nature of matter was thus verified. From the Davisson and Germer experiment, we get a value for the scattering angle θ and a corresponding value of the potential difference V at which the scattering of electrons is maximum. Thus the de-broglie equation was verified.
The experimental setup for the Davisson and Germer experiment is enclosed within a vacuum chamber. Thus the deflection and scattering of electrons by the medium are prevented. The main parts of the experimental setup are as follows:
● Electron gun: An electron gun is a Tungsten filament that emits electrons via thermionic emission i.e. it emits electrons when heated to a particular temperature.
● Electrostatic particle accelerator: Two opposite charged plates (positive and negative plate) are used to accelerate the electrons at a known potential.
● Collimator: The accelerator is enclosed within a cylinder that has a narrow passage for the electrons along its axis. Its function is to render a narrow and straight (collimated) beam of electrons ready for acceleration.
● Target: The target is a Nickel crystal. The electron beam is fired normally on the Nickel crystal. The crystal is placed such that it can be rotated about a fixed axis.
● Detector: A detector is used to capture the scattered electrons from the Ni crystal. The detector can be moved in a semicircular arc as shown in the diagram above.
Used to generate electricity in Solar Panels. These panels contain metal combinations that allow electricity generation from a wide range of wavelengths.
Motion and Position Sensors: In this case, a photoelectric material is placed in front of a UV or IR LED. When an object is placed in between the LED and sensor, light is cut off and the electronic circuit registers a change in potential difference
Lighting sensors such as the ones used in smartphone enable automatic adjustment of screen brightness according to the lighting. This is because the amount of current generated via the photoelectric effect is dependent on the intensity of light hitting the sensor.
Digital cameras can detect and record light because they have photoelectric sensors that respond to different colors of light.
X-Ray Photoelectron Spectroscopy (XPS): This technique uses x-rays to irradiate a surface and measure the kinetic energies of the emitted electrons. Important aspects of the chemistry of a surface can be obtained such as elemental composition, chemical composition, the empirical formula of compounds and chemical state.
Einstein’s Photoelectric equation: E = h𝝂.
De-Broglie’s relation, $\lambda=\frac{h}{p}$.
In this blog we have seen that light is not only a wave but it also has a particle nature. Also we have seen about the hypothesis and experiments which were used to prove the dual nature of radiation. We have seen about photoelectric effect which is a phenomenon associated with the dual nature of light and also Einstein’s photoelectric equation.
]]>We at Egnify wanted to share with you precise information about the changes that had taken place in the pattern of JEE (Main) 2020. National Testing Agency (NTA) conducts JEE (Main) in two slots each year, one in January and the other in April. This Computer Based Test is conducted separately for B.E./B.Tech (Paper-I) and B.Arch/B.Plan (Paper-II). Please note that the exam for B.Plan is separated from B.Arch this time by asking questions on planning separately for Paper-I.
S No. | Topic | 2019 | 2020 |
---|---|---|---|
1 | Duration of Exam | ||
Paper I (BE/B.Tech) | 3 Hrs | 3 Hrs | |
Paper II (B.Arch/B.Plan) | 3 Hrs | 3 Hrs | |
2 | Number of Questions | ||
Paper I (BE/B.Tech) | 30 Each in Mathematics, Physics & Chemistry | 25 each in Mathematics, Physics & Chemistry | |
Total 90 | Total 75 | ||
Single Choice Questions - 30 in each subject | Single choice questions - 20 in each subject | ||
Numerical/Integer type questions – 5 in each subject | |||
Paper II (B Arch) | B. Arch & B Plan | For B. Arch, | |
Maths – 30 | Math - 20 + 5 | ||
Aptitude – 50 | Aptitude – 50 | ||
Drawing – 2 | Drawing – 2 | ||
Total questions – 82 | Total questions - 77 | ||
For B. Plan, | |||
Math - 20 + 5 | |||
Aptitude – 50 | |||
Drawing – 25 | |||
Total questions - 100 |