The National Defence Academy (NDA) exam includes Physics as a crucial subject that covers a number of themes. Proficiency is required in understanding the fundamental formulas. The following article will help you navigate the topic of formulas of physics.
- About NDA Exam
For applicants to India's National Defence Academy, the NDA exam is a competitive entrance exam. It covers topics including physics, general ability, and maths. To pass this test, you must have a solid understanding of basic physics concepts.
- Physics section in NDA Exam
Numerous subjects are covered in physics in the NDA exam, such as nuclear physics, optics, electromagnetic, thermodynamics, and mechanics. In each of these categories, let's dissect the key formulas.
- Important formulas of Physics for NDA Exam. The list consists of formulas from NCERT 9th to 12th and also some important advanced formulas are given.
Chapter Motion –
- Motion is a change of position; it can be described in terms of the distance moved or the displacement done.
- The motion of the object can be uniform or non-uniform depending on whether its velocity is constant or changing.
- The speed of the object is the distance covered per unit of time, and velocity is the displacement per unit of time.
- The acceleration of the object is the change in velocity per unit time.
- Uniform and non-uniform motions of objects can be shown through graphs.
- The motion of an object moving at uniform acceleration can be described with the help of the following equations, namely—
- V = u+at;
- S = ut+1/2at2;
- 2as = v2-u2;
- Where ‘u’ is the initial velocity of the object means – with uniform acceleration ‘a’ for time ‘t’, ‘v’ is its final velocity, and ‘s’ is the distance it traveled in time ‘t’. If an object moves in a circular path with uniform speed, its motion is called ‘uniform circular motion’.
- Average speed= total distance traveled/ total time taken;
- Average velocity= [v+u]/2; [initial velocity+final velocity]/2;
- Acceleration= change in velocity/time taken; v-u/t;
The circumference of a circle of radius r is given by 2 r π. If the athlete takes t seconds to go once around the circular path of radius r,
- the speed v is given b---v=2πr/t;
Chapter—Forces and Laws Of Motion
First Law Of Motion: An object continues to be in a state of rest or of uniform motion along a straight line unless acted upon by an unbalanced force. The natural tendency of objects to resist a change in their state of rest or of uniform motion is called inertia. The mass of an object is a measure of its inertia. Its SI unit is kilogram (kg). The force of friction always opposes the motion of objects.
Second Law Of Motion: The rate of change of momentum of an object is proportional to the applied unbalanced force in the direction of the force. The SI unit of force is kg m s–2. This is also known as Newton and is represented by the symbol N. A force of one Newton produces an acceleration of 1 m s–2 on an object of mass 1 kg.
The momentum of an object is the product of its mass and velocity and has the same direction as that of the velocity. Its SI unit is kg m s–1. Third law of motion: To every action, there is an equal and opposite reaction and they act on two different bodies.
The Momentum, p of an object is defined as the product of its mass, m, and velocity, v.
- That is, p = mv;
The first law of motion can be mathematically stated from the mathematical expression for the second law of motion. Eq. F = ma;
- Or F = m[v-u]/t;
- Or Ft = mv – mu;
Chapter- Gravitation
The Law of Gravitation states that the force of attraction between any two objects is proportional to the product of their masses and inversely proportional to the square of the distance between them. The law applies to objects anywhere in the universe. Such a law is said to be universal.
Universal Law Of Gravitation is expressed as –
The law of gravitation states that the force of attraction between any two objects is proportional to the product of their masses and inversely proportional to the square of the distance between them. The law applies to objects anywhere in the universe. Such a law is said to be universal.
Gravitation is a weak force unless large masses are involved. The force of gravity decreases with altitude. It also varies on the surface of the earth, decreasing from poles to the equator. The weight of a body is the force with which the earth attracts it. The weight is equal to the product of mass and acceleration due to gravity. The weight may vary from place to place but the mass stays constant.
All objects experience a force of buoyancy when they are immersed in a fluid. Objects having a density less than that of the liquid in which they are immersed, float on the surface of the liquid. If the density of the object is more than the density of the liquid in which it is immersed then it sinks in the liquid.
The thrust on the unit area is called Pressure.
- Thus, Pressure= Thrust/Area;
Chapter- Work and Energy
Work done on an object is defined as the Magnitude of the Force multiplied by the distance moved by the object in the direction of the applied force. The unit of work is joule: 1 joule = 1 newton × 1 meter.
• Work done on an object by a force would be zero if the displacement of the object is zero
An object in motion possesses what is known as the kinetic energy of the object.
An object of mass, m moving with velocity v has a kinetic energy of =1/2mv2.
Power=Work/Time;
Let the work against gravity be W then,
The sum of the potential energy and kinetic energy of the object would be the same at all points. That is, potential energy + kinetic energy = constant or
An object having the capability to do work is said to possess energy. Energy has the same unit as that of work. An object in motion possesses what is known as the kinetic energy of the object. The energy possessed by a body due to its change in position or shape is called potential energy. The gravitational potential energy of an object of mass, m raised through a height, h from the earth’s surface is given by mgh.
According to the law of conservation of energy, energy can only be transformed from one form to another; it can neither be created nor destroyed. The total energy before and after the transformation always remains constant. Energy exists in nature in several forms such as kinetic energy, potential energy, heat energy, chemical energy etc. The sum of the kinetic and potential energies of an object is called its mechanical energy. Power is defined as the rate of doing work. The SI unit of power is watt. 1 W = 1 J/s
Chapter- Sound
Sound is produced due to the vibration of different objects. Sound travels as a longitudinal wave through a material medium. Sound travels as successive compressions and rarefactions in the medium. In sound propagation, it is the energy of the sound that travels and not the particles of the medium. The change in density from one maximum value to the minimum value and again to the maximum value makes one complete oscillation.
The distance between two consecutive compressions or two consecutive rarefactions is called the wavelength, λ. • The time taken by the wave for one complete oscillation of the density or pressure of the medium is called the time period, T. The number of complete oscillations per unit of time is called the frequency (ν). The speed v, frequency ν, and wavelength λ, of sound, are related by the equation, v = λν. The speed of sound depends primarily on the nature and the temperature of the transmitting medium. The law of reflection of sound states that the directions in which the sound is incident and reflected make equal angles with the normal to the reflecting surface at the point of incidence and the three lie in the same plane. For hearing a distinct sound, the time interval between the original sound and the reflected one must be at least 0.1 s.
Loudness is a physiological response of the ear to the intensity of sound. The amount of sound energy passing each second through unit area is called the intensity of sound. The audible range of hearing for average human beings is in the frequency range of 20 Hz – 20 kHz. Sound waves with frequencies below the audible range are termed “infrasonic” and those above the audible range are termed “ultrasonic”. Ultrasound has many medical and industrial applications.
- Frequency and time period are related as
Follows: v=1/T;
- The speed of sound is defined as the distance at which a point on a wave, such as a compression or a rarefaction, travels per unit of time.
We know,
- speed, v = distance / time = λ/T;
CLASS 10TH
Chapter- Light Reflection and Refraction
In a spherical mirror, the distance of the object from its pole is called the object distance (u). The distance of the image from the pole of the mirror is called the image distance (v). You already know that the distance of the principal focus from the pole is called the focal length (f). There is a relationship between these three quantities given by the mirror formula which is expressed as
As we have a formula for spherical mirrors, we also have a formula for spherical lenses. This formula gives the relationship between object distance (u), image distance (v), and the focal length (f ). The lens formula is expressed as
The Power P of a Lens of Focal Length f is given by---
- P=1/f;
Light seems to travel in straight lines. Mirrors and lenses form images of objects. Images can be either real or virtual, depending on the position of the object. The reflecting surfaces, of all types, obey the laws of reflection. The refracting surfaces obey the laws of refraction. New Cartesian Sign Conventions are followed for spherical mirrors and lenses. The focal length of a spherical mirror is equal to half its radius of curvature. The magnification produced by a spherical mirror is the ratio of the height of the image to the height of the object. A light ray traveling obliquely from a denser medium to a rarer medium bends away from the normal. A light ray bends towards the normal when it travels obliquely from a rarer to a denser medium. Light travels in a vacuum with an enormous speed of 3×108 m s-1. The speed of light is different in different media. The refractive index of a transparent medium is the ratio of the speed of light in a vacuum to that in the medium. In the case of a rectangular glass slab, the refraction takes place at both the air-glass interface and the glass-air interface. The emergent ray is parallel to the direction of the incident ray. Lens formula, 1 1 1 – = v u f, gives the relationship between the object distance (u), image distance (v), and the focal length (f) of a spherical lens. The power of a lens is the reciprocal of its focal length. The SI unit of power of a Lens is Dioptre.
Chapter-Electricity
A stream of electrons moving through a conductor constitutes an electric current. Conventionally, the direction of current is taken opposite to the direction of the flow of electrons. The SI unit of electric current is Ampere. To set the electrons in motion in an electric circuit, we use a cell or a battery. A cell generates a potential difference across its terminals. It is measured in volts (V).
Resistance is a property that resists the flow of electrons in a conductor. It controls the magnitude of the current. The SI unit of resistance is the ohm (Ω). Ohm’s law: The potential difference across the ends of a resistor is directly proportional to the current through it, provided its temperature remains the same. The resistance of a conductor depends directly on its length, inversely on its area of cross-section, and also on the material of the conductor. The equivalent resistance of several resistors in a series is equal to the sum of their individual resistances. A set of resistors connected in parallel has an equivalent resistance Rp given by 1 2 3 1 1 1 1 ... R R R R p = + + + n.
The electrical energy dissipated in a resistor is given by W = V × I × t n. The unit of power is Watt (W). One watt of power is consumed when 1 A of current flows at a potential difference of 1 V. The commercial unit of electrical energy is kilowatt hour (kWh). 1 kW h = 3,600,000 J = 3.6 × 106 J.
If a net charge Q, flows across any cross-section of a conductor in time t, then the current I, through the cross-section is— I=Q/t;
The SI unit of electric charge is Coulomb (C).
Potential difference (V) between two points = Work done (W)/Charge (Q) V = W/Q;
01volt= 01 joule/01 coulomb;
You will observe that the potential difference V is equal to the sum of potential differences V1, V2, and V3. That is the total potential difference across a combination of resistors in series is equal to the sum of potential difference across the individual resistors. That is,
- V = V1 + V2 + V3 ;
It is possible to replace the three resistors joined in series by an equivalent single resistor of resistance R, such that the potential difference V across it, and the current I through the circuit remains the same. Applying the Ohm’s law to the entire circuit, we have
- V = I R;
The rate at which electrical energy is dissipated or consumed in an Electric Circuit. This is also termed electric power. The power P is given by
- P = VI;
The SI unit of electric power is watt (W). It is the power consumed by a device that carries 1 A of current when operated at a potential difference of 1 V. Thus, 1 W = 1 volt × 1 ampere = 1 V A;
The electrical energy dissipated in a resistor is given by
- W = V × I ×t;
Chapter- Work, Energy, and Power
The work-energy theorem states that the change in kinetic energy of a body is the work done by the net force on the body. Kf - Ki = W.
Chapter-Laws Of Motion
Aristotle’s view that a force is necessary to keep a body in uniform motion is wrong. A force is necessary in practice to counter the opposing force of friction. Galileo extrapolated simple observations on the motion of bodies on inclined planes and arrived at the law of inertia. Newton’s first law of motion is the same law rephrased thus: “Everybody continues to be in its state of rest or of uniform motion in a straight line unless compelled by some external force to act otherwise”. In simple terms, the First Law is “If the external force on a body is zero, its acceleration is zero”.
Newton’s Second Law Of Motion: The rate of change of momentum of a body is proportional to the applied force and takes place in the direction in which the force acts.
The SI unit of force is Newton: 1 N = 1 kg m s-2. (a)
Newton’s third law of motion: To every action, there is always an equal and opposite reaction.
Law of Conservation of Momentum ---The total momentum of an isolated system of particles is conserved. The law follows from the second and third law of motion. Friction Frictional force opposes (impending or actual) relative motion between two surfaces in contact. It is the component of the contact force along the common tangent to the surface in contact.
SOME OTHER ADVANCED FORMULAS FOR THE NDA EXAM-
RELATIVE MOTION
LAWS OF MOTION
FRICTION
WORK
ENERGY AND POWER
GRAVITATION
HEAT AND TEMPERATURE
THERMODYNAMICS
ELECTRIC CURRENT
- There were important formulas and equations for the NDA exam and other defence exams as well.
- Having all the formulas in one place helps not only quick revision but also saves a lot of time by avoiding making notes again and again.
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