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What is the Universal law of gravitation?

Force of attraction between two masses \(m_1\) and \(m_2\) is given by, $$ F = \frac{m_1 m_2}{r^2}$$ Where, r is the distance between two masses \(m_1\) and \(m_2\). G is a constant, called the Universal gravitational constant. That is called Universal law of gravitation. Acceleration due to gravity ( variation formula ) If a body is falling freely, under the effect of gravity, then the acceleration in the body is called acceleration due to gravity. Variation in acceleration due to gravity with height Acceleration due to gravity at a height h above the surface of earth is, $$g' = g (1 - \frac{2h}{R_e})$$ Where, Re is the radius of the earth. g is the acceleratin due to gravity. Variation in acceleration due to gravity with depth Acceleration due to gravity at a depth d below the surface of earth is, $$g' = g (1 - \frac{d}{R_e})$$ Where, Re is the radius of the earth. g is the acceleratin due to gravity. Variation in acceleration due to gravity with rotatio…

What is the errors of measurement in physics?

Errors of measurement = True value of a quantity - Measured value of a quantity Suppose, the measured value of quantity be Am and the error in measurement be ΔA. Then the true value of the quantity can be written as At = Am ± ΔA Absolute error, Relative error and Percentage errorAbsolute errorSuppose a physical quantity be measured n times and the measured values be \( a_1, a_2, a_3 --- a_n \). The arithmetic mean of these values is given by,$$ a_m = \frac{a_1 + a_2 + a_3 + ... + a_n }{n}$$The absolute errors in the individual measurement values are$$ \Delta a_1 = a_m - a_1 $$$$ \Delta a_2 = a_m - a_2 $$$$ \Delta a_3 = a_m - a_3 $$.............$$ \Delta a_n = a_m - a_n $$Mean absolute errorMean absolute error \( \Delta a_m\) of a physical quantity is given by,$$ \Delta a_m = \frac {|\Delta a_1| + |\Delta a_2| + |\Delta a_3| +...+ |\Delta a_n|}{n} $$Relative errorRelative error \( R_e\) is given by,$$ \ R_e = \frac{\Delta a_m}{a_m}$$Percentage errorPercentage error \( p_e\) is g…

What is the energy?

The capacity to do work is called energy. Energy is a scalar quantity. The dimensional formula of the energy are the same as the dimensional formula of work i.e. [ M1L2T-2 ]. SI unit of energy is joule and CGS unit of energy is erg.Characteristics of energyThe entire matter possesss energy.Energy can neither be created nor be destroyed. The quantity of energy in the universe is constantEnergy can be transformed from one form to the other.The mechanical energy ( E ) of a body is given by, E = K + V
E = 1/2 (mv2) + mgh Where, K = Kinetic energy of a body. V = Potential energy. m = mass of a body. v = velocity of that body. g = acceleration due to gravity. h  =  height of a body.Kinetic energy of a moving body is given by following formula, K.E. = 1/2 ( mv2 ) or K.E. = p2/2m Where, m = Mass of the moving body. v = Velocity of that body. p = Linear momentum of that particle. Potential energy is given by V = mgh Where, m = mass of the body. h = height of that body. g = acce…

What is a semiconductor?

Those material, which have resistivity or conductivity intermediate to metals or insulator, called semiconductor. The band gap of semiconductor is less than 3 eV. The band gap of Ge and Si respectively 1.1 eV and 0.7 eV. Si, Ge, GaAs, CdTe etc are examples of semiconductors. The band gap of Ge and Si respectively 1.1 eV and 0.7 eV. Si, Ge and C are elemental semiconductor. Examples of compound semiconductors are following: Inorganic: Cds, GaAs, Cdse, InP etc.
Organic: Anthracene, doped pthalocyanines etc.
Organic Polymers: Polypyrolle, Polyaniline, Polythiophene etc. An intrinsic semiconductor is one which is made of the semiconductor material in its totally pure form and with no impurities or lattice defects. If we added small amount ( parts per million, ppm ) of suitable impurities in pure semiconductor , Then this process is called dopping and suitable impurity is called dopent. Dopped intrinsic or pure semiconductor is called extrinsic semiconductor. There ar…

What is the dimensional formula ?

The dimensional formula of the physical quantity is an expression which shows how and which of the base quantities represent the dimensions of a physical quantity. For example [ M0L2T0 ] is the dimensional formula of velocity. similarly, [ M0L3T0 ] is the dimensional formula of volume. Dimensional formula of all important physical quantities. Dimensional formula of major physical quantities e.g. area, volume, velocity, acceleration, force, momentum, impulse, work, energy, power, surface tension etc. are following: Physical quantityDimensional formulaAccelerationM0L1T-2Acceleration due to gravityM0L1T-2AngleM0L0T0Angular accelerationM0L0T-2Angular displacementM0L0T0Angular frequencyM0L0T-1Angular impulseM1L2T-1Angular momentumM1L2T-1Angular velocityM0L0T-1AreaM0L2T0Avogadro's numberM0L0T0Binding energy of nucleusM1L2T-2Boltzmann constantM1L2T-2K-1Bulk modulusM-1L0T-2CapacityM-1L-2T4A2Capacitative reactanceM1L2T-3A-2Centripetal accelerationM0L1T-2ChargeM0L0T1A1Coefficient of ela…

How many fundamental and supplementary units in SI?

In SI, there are seven base ( fundamental ) units and two supplementary units.
Base unit

Physical quantity


Unit


Symbol




Mass


Kilogram


kg




Length


Metre


m





Time


Second


s





Temperature


Kelvin


K





Electric current


Ampere


A





Luminous intensity


Candela


cd





Quantity of matter


Mole


mol




Supplementary units


Physical quantity


Unit


Symbol




Plane angle


Radian


rad





Solid angle


Steradian


sr



Conversion factor
Conversion of length

1 centimetre = 10-2 metre
1 millimetre = 10-3metre
1 micrometre = 10-6metre
1 nanometre = 10-9 metre
1 angstrom= 10-10 metre
1 fermi = 10-15 metre
1 kilometre = 103 metre
1 austronomical unit = 1AU=1.496 × 1011 metre
1 light year = 1 ly = 9.461 ×1015metre
1 mile = 1.609 ×103 metre
1 yard = 0.9144 metre
1 inch = 0.0254 metre


Conversion of time

1 mili second= 10-3 second
1 micro second = 10-6 second
1 neno second = 10-9 second
1 hour = 60 minute = 3600 second
1 day = 24 hours =86400 second
1 year = 365 day = 3.156× 107 second
1 sec = 10-8second


Conversion of mass

1 gram = 10 -3 kg
1 quintal = 100 kg
1 tonne = 1000 kg
1 slug = 14.59…

Logrithm formula

Formulae of Logarithm

loga mn = loga m + loga n
loga m/n = loga m - loga n
loga mn = n loga m
loga m= logb m × loga b
loge m = 2.3026 log10 m
log10 m = 0.4343 loge m

Logrithmic Series

loge ( 1+x ) = x - x2/2 + x3/3 - x4/4 +......
loge ( 1-x ) = -[x + x2/2 + x3/3 + x4/4 +......]
loge ( 1+x ) / ( 1-x ) = 2 [x + x3/3 + x5/5 +......]

Algebra formula

Factors ( a+b )2 = a2 + b2 + 2ab ( a-b )2 = a2 + b2 - 2ab ( a2 - b2) = ( a+b ) ( a-b ) ( a2 + b2 ) = ( a+b )2- 2ab ( a+b )3 = a3 + b3 + 3ab( a+b ) ( a-b )3 = a3 - b3 - 3ab( a-b ) ( a+b+c)2 = a2 + b2 + c2 +2(ab + bc + ac ) a3 + b3 + c3 - 3 abc = ( a+b+c ) ( a2 + b2 + c2 – ab – bc – ac ) ( a+b )4 = a4 + b4 + 2ab ( 2a2 + 3ab + 2b2) ( a-b )4 = a4 + b4 - 2ab ( 2a2 + 3ab - 2b2 )
Exponential Series

ex = 1 + x/1! + x2 /2! + x3/3! + .....
e = 1 + 1/1! + 1/2! + 1/3! + ....
e = 2.7182
e-x = 1 - x/1! + x2 /2! - x3/3! + .....
ex + e-x = 2 [ 1 + x2/2! + x4/4 + .....]



Binomial Theorem

( 1+x )n = 1+nx+[n( n-1)/2!] .x2 + [n(n-1)(n-2)/3!].x3 +......
( 1+x )-n = 1-nx+[-n( n+1)/2!] .x2 - [n(n+1)(n+2)/3!].x3 +......

If x<<1
then x2,x3,.... is negligible. so:

(1+x ) -n ≈ 1-nx
(1-x ) n ≈ 1-nx
(1-x ) -n ≈ 1+nx

Differentiation formula

Fomulae of Differentiation d⁄dx (c) = 0   Where c is constant.d⁄dx (cx) = c   Where c is constant.du⁄dt = du⁄dx ⋅ dx⁄dtd⁄dx (u+v) = du⁄dx + dv⁄dxd⁄dx (uv) = u dv⁄dx + v du⁄dxd⁄dx ( xn ) = n xn-1  Where n is real number.d⁄dx un = n un-1du⁄dx   Where u is function of x.d⁄dx sin x = cos x d⁄dx cos x = -sin x d⁄dx tan x = sec2 x d⁄dx cot x = - cosec2 x d⁄dx sec x = tan x sec x d⁄dx cosec x = - cot x cosec x d⁄dx loge x = 1⁄xd⁄dx loge u = 1⁄udu⁄dxd⁄dx ( ex ) = exd⁄dx ( eax ) = a eaxd⁄dx sin ax = a cos ax d⁄dx sin (ax+b) = a cos (ax+b) d⁄dx cos ax = - a sin ax d⁄dx cos (ax+b) = - a sin (ax+b)

How many elements are there in the periodic table?

There are 118 chemical elements in the periodic table. List of all chemical elements is given below. Elements of periodic tableAtomic numberElement SymbolElement Name1 HHydrogen2HeHelium3LiLithium4BeBeryllium5BBoron6CCarbon7NNitrogen8OOxygen9FFluorine10NeNeon11NaSodium12MgMagnesium13AlAluminium14SiSilicon15PPhosphorus16SSulfur17ClChlorine18ArArgon19KPotassium20CaCalcium21ScScandium22TiTitanium23VVanadium24CrChromium25MnManganese26FeIron27CoCobalt28NiNickel29CuCopper30ZnZinc31GaGallium32GeGermanium33AsArsenic34SeSelenium35BrBromine36KrKrypton37RbRubidium38SrStrontium39YYttrium40ZrZirconium41NbNiobium42MoMolybdenum43TcTechnetium44RuRuthenium45RhRhodium46Pd Palladium 47 AgSilver48CdCadmium49InIndium50SnTin51SbAntimony52TeTellurium53IIodine54XeXenon55CsCaesium56BaBarium57LaLanthanum58CeCerium59PrPraseodymium60NdNeodymium61PmPromethium62SmSamarium63EuEuropium64GdGadolinium65TbTerbium66DyDysprosium67HoHolmium68ErErbium69TmThulium70YbYtterbium71LuLutetium72HfHafnium73TaTantalum74WTungsten75R…

Integration formula

Integration formula

∫ xn dx = xn+1⁄n+1   where ( n≠ -1 )

∫ dx = x

∫ c xn dx = c xn+1⁄n+1   where ( n≠ -1 )

∫ 1⁄x dx = ln x

∫ sin x dx = - cos x

∫ cos x dx = sin x

∫ ex dx = ex

∫ ( u+v ) dx = ∫ u dx + ∫ v dx

∫ sec2 x dx = tan x

∫ cosec2 x dx = - cot x

∫ sec x tan x dx = sec x

∫ cosec x cot x dx = - cosec x

∫ eax dx = 1⁄a eax

∫ sin ax dx = - 1⁄a cos ax

∫ sin (ax+b) dx = - 1⁄a cos (ax+b)

∫ cos ax dx = 1⁄a sin ax

∫ cos (ax+b) dx = 1⁄a sin (ax+b)

Trigonometry formula

Basic trigonometry formula

Perp./Hyp. = sin θ
Base/Hyp. = cos θ
Perp./Base = tan θ
Base/Perp. = cot θ
Hyp./Base = sec θ
Hyp./Perp. = cosec θ

Baudhayana formula
( Hyp. )2 = ( Base )2 + ( Perp.)2
Some common trigonometric Formulas

sin(A+B) = sin A cos B + cos A sin B
sin(A-B) = sin A cos B - cos A sin B
cos(A+B) = cos A cos B - sin A sin B
cos(A-B) = cos A cos B + sin A sin B

sin 2A = 2 sin A cos B
cos 2A = cos2 A - sin2 A
cos 2A = 1 - 2 sin2 A
sin(A+B) + sin(A-B) = 2 sin A cos B
sin(A+B) - sin(A-B) = 2 cos A sin B
cos(A+B) + cos(A-B) = 2 cos A cos B
cos(A+B) - cos(A-B) = -2 sin A sin B

Trigonometric Ratios
Trigonometry ratio table:
Table of trigonometrical ratios of some standard angels:




Angle


sin θ


cos θ


tan θ




00


0


1


0




300


$$\frac{1}{2}$$


$$\frac{\sqrt{3}}{2}$$


$$\frac{1}{\sqrt{3}}$$




450


$$\frac{1}{\sqrt{2}}$$


$$\frac{1}{\sqrt{2}}$$


1




600


$$\frac{\sqrt{3}}{2}$$


$$\frac{1}{2}$$


$$\sqrt{3}$$




900


1


0


$$\infty $$




1200


$$\frac{\sqrt{3}}{2}$$


$$-\frac{1}{2}$$


$$-\sqrt{3}$$




1350


$$\frac{1}{\sqrt{2}}$$


$$-\frac{1}{\sqrt{2…

What are the laws of motion?

Galileo's law of inertia
A body continues in its state of rest or constant velocity along the same straight line, unless not disturbed by some external force. This is Galileo's law of inertia.
Newton's laws of motion
Newton's gives three law of motion:
1. Newton's first law motion
A body continues in its state of rest or constant velocity along the same straight line, unless not disturbed by some external force. This is Newton's first law motion.
2. Newton's second law motion
Time-rate of change of momentum is proportional to the applied external force. This is Newton's second law motion
3. Newton's third law motion
To every action there is always equal and opposite reaction. This is Newton's third law motion.
Linear momentum
Linear momentum of a moving particle is given by,

$$ \vec{p} = m\vec{v}$$

Where m is the mass of moving particle with velocity \( \vec{v}\)
Force
Force on a particle having mass m is given by,

$$\vec{F} = m\vec{a}$$

Where, \(\vec{a}\) is th…

What is rigid body?

A system of large number of particles in which the distance between any two particles remains fix throughout the motion is called rigid body.

Moment of inertia
Moment of inertia I is given by,
$$ I = \Sigma m_i r_i^2$$

Torque
If a force \(\vec{F}\) acts at a point, whose position vector is \(\vec{r}\); the torque due to force
$$\vec{\tau} = \vec{r} \times \vec{F}$$

Angular displacement
Angular displacement is given by, $$ \theta = \frac{s}{r} $$

Angular velocity
Angular velocity is given by,
$$\omega = \frac{d\theta}{dt}$$

Angular acceleration
Angular accceleration is given by,
$$\alpha = \frac{d\omega}{dt}$$
SI unit of angular acceleration is rad s-2. Its dimensional formula is [M0L0T-2].

Angular momentum
Angular momentum is given by $$\vec{L} = \vec{r} \times \vec{p}$$ Where \(\vec{p}\) is linear momentum of the particle and \(\vec{r}\) is position vector of the particle.

Relation between torque and angular momentum
Relation between torque and angular momentum is given $$\tau = \frac{d\vec{L}}{dt}$$


Ta…

What is the ideal gas equation?

The equation of state of an ideal gas is given by,
PV = nRT
Where, n is the number of moles of the gas and R is the gas constant for one mole of the gas.

The gas law
Boyle's law
If \(\mu\) and T are constant then idael gas equation becomes, $$PV = Constant $$ or $$ P \propto \frac{1}{V} $$ This is the Boyle's law.

Charle's law
If \(\mu\) and P are constant then idael gas equation becomes,
$$ V \propto T $$ This is the Charle's law.

Gay lussac's law
If \(\mu\) and V are constant then idael gas equation becomes,
$$ P \propto T $$ This is the Gay lussac's law.

Specific heat capacity
Specific heat capacity is given by,
$$ s = \frac{S}{m}$$
Where, S is heat capacity and $latex m$ is the mass of substance.
The unit of specific heat capacity is J kg-1 k-1

Degrees of freedom

Number of degrees of freedom of a system is given by following,
N = 3A - R
Where,
A is the number of particles in the system and R is the number of independent relations among the particles.



For mono atomic gases, the…

What are the different types of waves?

Basically waves can be three types:

Mechanical waves
Electromagnetic waves
Matter waves

Mechanical waves
Waves which can be produced and propagated only in a material medium are known as mechanical waves.
Water waves, sound waves, waves on string, seismic waves etc. are the example of mechanical waves.
The propagation of mechanical wave depends on the elasticity and inertia of the medium. Thus, these waves are known as elastic waves.

Mechanical waves are two types: Transverse waves and longitudinal waves.
Transverse waves
Waves on the water surface, light waves, wave generated on the string etc are the examples of transverse waves.
Longitudinal wave
Sound wave propagated in air is the example of longitudinal waves.
Electromagnetic waves
Those waves which requires no material medium for their production and propagation, this means it propagates in vacuum. Such waves are called electromagnetic waves.
Visible light, ultraviolet light, radio waves, microwaves, X-rays etc are the examples of electromag…

What is an electric charge?

Charge is the properties of matter. According to Benjamin franklin there are two types of charge, (1) Positive charge and (2) Negative charge.
Electric charge is a scalar quantity.
In SI System, the unit of Electric charge is Coulomb.
The dimensional formula of Electric charge is [ M0L0T1A1 ]

Coulomb's law
The force on a test charge Q due to a single point charge q is given by coulomb's law $$\vec{F} = \frac{1}{4\pi \epsilon_0 } \frac{Qq}{r^2} \hat{r}$$ Where r is the distance between Q and q and ε0 is the permitivity of the free space.

Electric field
The force per unit charge that would be exerted on a test charge is called electric field.

Electric flux
$$\Delta \phi = \vec{E}.\Delta S$$

Gauss's law
Electric flux ( φ ) through a closed surface (S) enclosing the total charge (q) is given by,
$$\phi = \frac{q}{\epsilon_0}$$
That is is the Gauss's law.

Electric dipole
If two equal and opposite charges +q and -q are separated by a distance 2d, then this arrangement is called electric…

What is scalar and vector quantity?

The physical quantity which have only magnitude but no direction, are called scalar quantity.
Mass, length, time, speed, volume, density, pressure, temperature, work, energy, power, electric current, electric charge, electric potential, electric flux etc are the examples of scalar quantity.


Scalar or Dot Product
Dot product of two vectors A and B is represented by,
A .B = AB cosθ


Where θ is angle between two vectors A and B.

•   If two vectors A and B are parallel, then θ = 0०


A.B = AB
For unit vectors,

î . î = &jcirc; . &jcirc; = k.k = 1


•   If two vectors A and B are mutually perpendicular, then θ = 90०

A.B = 0

For unit vectors,

î . &jcirc; = &jcirc; . k = k.i = 0


•   If two vectors A and B are anti parallel, then θ = 0०


A.B = - AB

•   Properties of dot product


1.Dot product of two vectors is commutative.

A . B = B . A

2.Dot product is distributive.

A . ( B + C ) = A . B + A . C

•   Dot product of two vectors A and B in component form
A .…

What is work in physics?

What is work?
Scalar product of force and displacement is called work.
$$ W = \vec{F}.\vec{S}\cos \theta $$
Work is a scalar quantity. The dimensional formula of work is [ M1L2T-2 ]. SI unit of work is joule. CGS unit of work is erg.
Relation between joule and erg is
1 joule = 107 erg.
In terms of rectangular components, work is
W = x Fx + y Fy + z Fz
Types of work
Positive work
If angle between \(\vec{F}\) and \(\vec{S}\) lies between 00 and 900, then work done is positive.
Negative work
If angle between \(\vec{F}\) and \(\vec{S}\) lies between 900 and 1800, then work done is negetive.
Negative work
The work done is zero, if

there is no displacement
no force is acting on the body
angle between \(\vec{F}\) and \(\vec{S}\) is 900

What is the position vector of centre of mass of the two particle system?

For two particle system, the position vector of centre of mass of the two particle system is given by,
$$\vec{r} = \frac {m_1 \vec{r_1} + m_2 \vec{r_2}}{m_1+m_2}$$

For two particle system, velocity of centre of mass is given by,
$$\vec{v_c} = \frac {m_1 \vec{v_1} + m_2 \vec{v_2}}{m_1+m_2}$$
Whewe,
\(m_1\) and \(m_2\) are the masses of two particles.
\(\vec{r_1}\) and \(\vec{r_2}\) are the position vector of the particles \(m_1\) and \(m_2\) respectively.
\(\vec{v_1}\) and \(\vec{v_2}\) are velocities of the particles \(m_1\) and \(m_2\) respectively.

What is logic gates?

Truth table of AND Gate:



INPUT
OUTPUT



A
B
Y = A.B


0
0
0


0
1
0


1
0
0


1
1
1



Truth table of NOT Gate.



INPUT
OUTPUT


A
Y
0
1
1
0


Truth table of OR Gate.

INPUT
OUTPUT
A
B
Y = A+B
0
0
0
0
1
1
1
0
1
1
1
1



Truth table of NAND Gate.

INPUT
OUTPUT
A
B
Y

0
0
1

0
1
1

1
0
1

1
1
0



Truth table of NOR Gate.



INPUT
OUTPUT
A
B
Y

0
0
1

0
1
0

1
0
0

1
1
0




Truth table of XOR Gate.



INPUT
OUTPUT
A
B
Y

0
0
0

0
1
1

1
0
1

1
1
0