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Fundamental Physical Quantities:
S.No  Fundamental Physical Quantity  Formula  Dimensional Formula  S.I Unit of physical quantity 
1.  Mass  Amount of matter in the object  M  kg 
2.  Length  L  meter  
3.  Time  T  sec  
4.  Electric current  I or A  ampere  
5.  Amount of substance  N  mole(mol  
6.  Luminous intensity  J  candela(cd)  
7.  Temperature  K or  Kelvin 
Derived Physical Quantities:
S.No  Derived Physical Quantity  Formula  Dimensional Formula  S.I Unit of physical quantity 
1.  Area  []  
2.  Volume  []  
3.  Density  []  
4.  Specific Gravity  []  No units  
5.  Frequency  []  hertz  
6.  Angle  No units  
7.  Velocity  m/sec  
8.  Speed  m/sec  
9.  Areal velocity  
10.  Acceleration  
11.  Linear momentum  kg m/sec  
12.  Force  kgm/ or Newton  
13.  Weight  w=mg  kgm/ or Newton  
14.  Moment of force/Torque/Couple  kg  
15.  Impulse  kg m/sec or Ns  
16.  Pressure  N/ or Pa  
17.  Work  Nm or Joule  
18.  Kinetic Energy  joule  
19.  Potential Energy  mgh  joule  
20.  Gravitational constant  
21.  Gravitational field strength  
22.  Gravitational Potential  
23.  Force constant (k)  
24.  Power  W or J/sec  
25.  Moment of Inertia ( I )  kg  
26.  Stress  N/ or Pa  
27.  Strain  No units  
28.  Modulus of Elasticity  N/ or Pa  
29.  Poission’s Ratio  σ =1  No units  
30.  Velocity gradient  
31.  Coefficient of dynamic viscosity  kg(or) Nsec/$latex \m^2$ (or)pascalsec (or)poiseuille  
32.  Surface Tension  ,N/m  
33.  Angular displacement ()  no Units  
34.  Angular velocity(ω)  rad/sec  
35.  Angular acceleration(α)  rad/  
36.  Angular momentum  Iω  
37.  Angular Impulse  Iω  
38.  Temperature  or K  kelvin or degree Celsius  
39.  Coefficient of linear expansion(α)  /kelvin  
40.  Specific heat  
41.  Latent heat  
42.  Entropy  
43.  Thermal capacity  
44.  Gas constant  
45.  coefficient of thermal conductivity  
46.  Pole strength  Am  
47.  Magnetic Moment  
48.  Magnetic flux  weber ; ;J/Amp  
49.  Magnetic field,magnetic flux density (B)  Tesla;  
50.  Permeability of free space  
51.  Magnetic susceptibilty also called volumetric or bulk susceptibility χ_{m}  χ_{m} = μ_{r} − 1  no units  
52.  Electric Charge  Amp sec , coul  
53.  Electric potential  Volt  
54.  E.M.F  Volt  
55.  Electric Capacity  Farad  
56.  Electric Resistance  Ohm (Ω) or volt/amp  
57.  Resistivity  Ohm mt (Ωm)  
58.  Conductivity  1/  Siemens/m  
59.  Permittivity 

farad/m  
60.  Electric conductance  Siemens (or) mhos  
61.  Electric power  Watt  
62.  Electrical Impedance(Z)  Ohm (Ω) or volt/amp  
63.  Electrical admittance  1/Z(Reciprocal of electric impedance)  Siemens (or) mhos  
64.  Self Inductance(L)  weber/amp or Henry  
65.  Boltzmann’s constant  J/kelvin  
66.  Stefan’s constant  
67.  Coefficient of friction  =,N=Normal reaction  dimension less scalar  no units 
68.  Dielectric constant  It is also called relative permittivity  dimension less  no units 
69.  Planck’s constant  J.sec (or) eV.sec  
70.  Refractive index  μ  no units  
71.  Focal length(f)  Distance between center of the lens(mirror) to its focus  L  meter 
72.  Power of a lens (P)  The reciprocal of the focal length of a lens in meters is called power of a lens; p=1/f  diaptors  
73.  Wave number  No.of waves/distance  
74.  Wave length  Length of a wave  L  meter 
But, the addition of vectors is complicated.If we add two vectors of magnitudes 2 and 8 the resultant vector’s magnitude will be 6 or 10 or any value between 6 and 10 depending on the directions of the vectors we are adding.
i) If the two given vectors are acting in same direction then the magnitude of the resultant vector will be 10 units,
ii) If the two given vectors are acting in opposite directions then the magnitude of resultant vector will be 6 units,
iii) If the two given vectors are acting in different directions then the magnitude of the resultant vector will be between 6 and 10.
How to add two given vectors(Geometrical representation): Suppose and are two given vectors.
i)If the two vectors are acting in the same direction,take the first vector Suppose , to the terminal point of connect the initial point of .
We get + = .
The magnitude of resultant vector will be equal to the sum of magnitudes of and
i.e When two vectors are acting in same direction the “sum of the magnitudes of the vectors = Magnitude of resultant vector”
AB+CD = AD
ii)If the two vectors are acting in different directions in that case the procedure of addition will be same but the direction and magnitude of resultant vector will be different.Suppose and are two given vectors acting in different directions as shown in the below fig(a).
To add these two vectors connect the initial point C of IInd vectors to the terminal point B of First vector .Now join the initial point A of first vector with the terminal point D of the second vector .The vector taken in reverse order (closing side taken in reverse order) represents the resultant vector both in magnitude and direction.
I.e When two vectors are acting in different directions the “Sum of the magnitudes of the vectors > Magnitude of resultant vector”.
Laws of vector addition:
i) Vector addition is commutative + = +
Proof:Suppose = and = are two given vectors.Now let us add these two vectors. To add
them let us connect the initial position of to the terminal point of in anti clock wise direction,now closing side OB taken in the reverse order represents the resultant vector .
Now draw a vectors parallel to and and complete the parallelogram OABC.From the Fig(ii) = = and = = .
From triangle OAB + =
i.e + = – – – – – – – – – – – – (1)
From triangle OCB + =
i.e + = – – – – – – – – – – – – (2)
from eq(1) and (2) we get + = +
Hence vector addition is commutative.
ii) Vector addition is associative: Let = , = and = be three different vectors.
To add the given three vectors , and we have to connect the initial point of to the terminal point of and the initial point of to terminal point of .The closing side taken in reverse order represents the resultant vector.
Hence resultant = .
Proof:To add three vectors we have to first add two vectors and to sum vector we will add the third vector.
Form fig(ii) from the triangle OAB + = = ( + ) – – – (1)
from triangle OBC + = = – – – – – – – – – – – – (2)
substitute the value and = ( + ) from eq(1) to eq(2)
we get ( + ) + = = – – – – – (A)
From triangle ABC + =
i.e ( + ) = – – – – – – – – – (3)
From triangle OAC + = = – – – – – – – – (4)
solving eq(3) and eq(4) we get + ( + ) = = – – – – – – – (B)
Comparing eq(A) & eq(B) we get ( + ) + = + ( + )
Hence,vector addition is associative.
Subtraction of Vectors: Subtraction of vectors is also a form of addition.Addition of two vectors acting in opposite direction is called subtraction of vectors.
Suppose as in fig(i) = and = are two vectors, to subtract from we have to add the negative vector of to , i.e – = + ( –).
In the fig (ii) we have drawn = () negative vector of = , now connect the initial point of
latex \overline{BE}$ to the terminal point of . From the resultant vector of addition of these two vectors is .
Therefore + =
i.e + ( ) = – = .
* Subtraction of vectors is not commutative – –
C.R.MARKETING  4890/3/1  NEAR SBM GARDENS  MANJEERA NAGAR  SANGAREDDY  DIST:MEDAK 
C.R.ENTERPRISES  4890/3/1  NEAR SBM GARDENS  MANJEERA NAGAR  SANGAREDDY  DIST:MEDAK 
vrd  srd  dgi 
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VECTORS
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Tue, 17 May 2011 15:29:40 +0000
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]]>Physical quantities are classified in to two categories i) Scalar quantities ii)Vector quantities
1. Scalar quantities or Scalars :The physical quantities which have magnitude but no direction are called scalar quantities or scalars.
Ex:Length,mass,time,area,volume,speed,energy,work,temperature etc
2.Vector quantities or Vectors:The physical quantities which posses magnitude as well as direction are called Vector quantities or Vectors.
Ex:Displacement,velocity,acceleration,momentum,force etc
Geometrical representation of vectors :A vector is geometrically represented by a directed line segment. The length of the directed line segment is called magnitude of the vector and the direction of the line segment represents the direction of the vector quantity.
Ex: If a body starts from a point O after traveling for certain time it reaches its destination point A.Then the displacement of the body is represented by the directed line segment OA . The Length of the straight line OA represents the magnitude of the displacement of the body, and the direction of the line segment from O towards A represents the direction of displacement of the body. Vector is read as AB bar.The magnitude of is written as and read as modulus of .
Types of Vectors :
1.Coinitial vectors: All those vectors whose initial points are same, such vectors are called co initial vectors. Ex: OA,OB,OC, OD ,OE all these vectors have initial point O. Hence these are coinitial vectors.
2.Coterminal vectors :All those vectors whose terminal (end) points are same,such vectors are called co terminal vectors.
Ex: The terminal point of all these vectors ,, , is Same point P. Hence, these vectors are called coterminal vectors.
3. Coplanar Vectors:The vectors which lie in the same plane are called Coplanar Vectors.
Ex:a) All the vectors which lie in XY plane are called coplanar irrespective of their magnitudes
and directions. b) all the vectors which lie in YZ plane are coplanar with respect to one another.
4.Null vectors: Any vector which has direction but no magnitude is called a null vector. For a null
vector its initial point and the terminal point will be same .
Ex: , . ………………. Are null vectors.
5.Unit Vector: Any vector of unit magnitude is called unit vector.If is a vector,it’s unit vector is denoted by .This () is read as a cap.
If you divide a vector with its magnitude we get the unit vector of that vector.
Therefore unit vector
where is called the magnitude of vector.
Every vector will have its own unit vector.Unit vector of any vector will be of unit magnitude irrespective of the magnitude of the original vector.
If is a vector its unit vector will be ,the direction of and will be same.Similarly if is a vector its unit vector will be ,the direction of and will be same.
Three mutually perpendicular axes OX,OY AND OZ form the Cartesian coordinate system.The unit vectors along X,Y and Z axis are represented by , and respectively.
6.Like vectors : All the vectors acting in the same direction are called like vectors.
are acting in the same direction ,hence and are like vectors.
Note: Like vectors will be always i)parallel to one another ii) will be acting in the same direction , but iii)not necessarily be of the different magnitudes.
7. Unlike Vectors : Any two vectors parallel to one another and acting in opposite directions are called unlike vectors.
The given vectors and are acting in the opposite directions , hence and are unlike vectors.
Note: Unlike vectors will be always i)parallel to one another ii) will be acting in the opposite directions , but iii)not necessarily be of the different magnitudes.
8. Negative Vector : If = is a vector,then = – will be the negative vector of .
i)The original vector and it’s negative vector – will be of same magnitude i.e = ii) they will be opposite to one another. iii) every vector will have a negative vector.
9. Axial Vectors or (One dimensional Vectors) : The vectors acting along X,Y or Z axes ( or) vectors parallel to any one of the Axis are called axial vectors (or) one dimensional vectors.
9(i). Vectors parallel to X axis : In the Fig(1) all the vectors = , = and
= are parallel to X axis. These vectors , and are called axial vectors parallel to Xaxis. If the magnitudes of vectors , and are =a , =b and , = c ,then we can represent the axial vectors as = a , = b and = c .
Ex: i)5 is a vector of 5units magnitude working along Xaxis or parallel to Xaxis in positive direction. ii) 8/5 is a vector of 8/5 units magnitude working along Xaxis or parallel to Xaxis in positive direction. iii) 9 is a vector of 9units magnitude working along Xaxis or parallel to Xaxis in negative direction. iv)a is a vector of a units magnitude working along Xaxis or parallel to Xaxis in positive direction.
9(ii). Vectors parallel to Y axis : In the Fig(2) all the vectors = , = and
= are parallel to Y axis. These vectors , and are called axial vectors parallel to Yaxis. If the magnitudes of vectors , and are =a , =b and , = c ,then we can represent the axial vectors as = a , = b and = c .
Ex: i)3 is a vector of 3units magnitude working along Yaxis or parallel to Yaxis in positive direction. ii) 5/3 is a vector of 5/3units magnitude working along Yaxis or parallel to Yaxis in positive direction. iii) 7 is a vector of 7units magnitude working along Yaxis or parallel to Yaxis in negative direction. iv)b is a vector of b units magnitude working along Yaxis or parallel to Yaxis in positive direction.
9(iii). Vectors parallel to Z axis : In the Fig(3) all the vectors = , = and
= are parallel to Z axis. These vectors , and are called axial vectors parallel to Zaxis. If the magnitudes of vectors , and are =a , =b and , = c ,then we can represent the axial vectors as = a , = b and = c .
Ex: i)6 is a vector of 6units magnitude working along Zaxis or parallel to Zaxis in positive direction. ii) 8/5 is a vector of 8/5 units magnitude working along Zaxis or parallel to Zaxis in positive direction. iii) 4 is a vector of 4units magnitude working along Zaxis or parallel to Zaxis in negative direction. iv)c is a vector of c units magnitude working along Zaxis or parallel to Zaxis in positive direction.
10.Two dimensional vectors (or) Plane vectors:The vectors acting in XYPlane or YZPlane or ZXPlane are known as two dimensional vectors or also known as vectors in a plane.
10(i).Vectors in XYPlane: In the given Fig(i) = is a vector working in XYPlane.It’s Xcomponent is and Y component is .So we can express the given vector as the sum of the component vectors.
= + .
There fore the vectors acting in XYPlane will have only two components Xcomponent and Ycomponent.These XYplane vectors can also be represented in Cartesian coordinate form. =( , , 0).
Note: If X,Y coordinates exists(not equal to zero) and the Z coordinates does not exist(=0), such vectors will be in XY plane.
10(ii).Vectors in YZPlane: In the given Fig(ii) = is a vector working in YZPlane.It’s Ycomponent is and Z component is .So we can express the given vector as the sum of the component vectors.
= + .
There fore the vectors acting in YZPlane will have only two components Ycomponent and Zcomponent.These YZplane vectors can also be represented in Cartesian coordinate form. =(0, , ).
Note: If Y,Z coordinates exists(not equal to zero) and the X coordinates does not exist(=0), such vectors will be in YZ plane.
10(iii).Vectors in XZPlane:
In the given Fig(i) = is a vector working in XZPlane.It’s Xcomponent is and Z component is .So we can express the given vector as the sum of the component vectors.
= + .
There fore the vectors acting in XZPlane will have only two components Xcomponent and Zcomponent.These XZplane vectors can also be represented in Cartesian coordinate form. =( ,0, ).
Note: If X,Z coordinates exists(not equal to zero) and the Y coordinates does not exist(=0), such vectors will be in XZ plane.
11.Space Vector: If any vector possess components along all the three axes X,Y and Z such vectors are called space vectors.
= + + .These space vectors can also be represented in Cartesian coordinate form. =( ,, ).
In the given fig is a space vector .Where OC = , OA = and OG = .Hence = = + + .
Filed under: Vectors Tagged: Types of vectors ]]>
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Physics in Every Day Life
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Sun, 15 May 2011 16:15:13 +0000
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]]>1.Does hot water put out a fire faster than cold water?
Ans:Yes.When fire is caught if you sprinkle cold water,the water first absorbs heat from the flame and gets heated to boiling point.Then it absorbs heat further and becomes vapor.Once it is vaporized it occupies that region around the flame.Because of this,availability of oxygen around the flame will be reduced drastically and the fire will put out.
Instead of cold water if hot water is sprinkled it vaporizes faster than cold water hence the fire will put out faster in this case.
2.What is Heat?
Ans:Heat is a form of energy,which gets transmitted between two bodies or two regions when they at at different temperatures.Heat always flows from a body at high temperature to a body at low temperature.
Filed under: Expansion of Gases, Expansion of Liquids, GENERAL, Physics in Every Day Life (Answers to common Questions) ]]>
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Types of Units
https://gyaunnrraje.wordpress.com/2010/04/04/typesofunits/
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Sun, 04 Apr 2010 17:07:40 +0000
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]]>Generally we can use any convenient unit to measure a physical quantity depending on how much magnitude we are measuring or in which system of units we want to measure it.
What kind of unit we should use?
The unit i) must be accepted internationally.
ii) Should be reproducible.
iii) Should be invariable.
iv) Should be easily available.
v) Should be consistent.
vi) Should be large, if the physical quantity to be measured is a big quantity.
Ex: To measure larger lengths we use units like Km, mt etc, to measure large magnitude of time we use units like hour , day ,week, month , year etc.
vii) Should be small if the physical quantity to be measured is small.
Ex: To measure small time we use units like millisecond, microsecond etc
To measure small lengths we use units like millimeter, centimeter etc.
Types of physical Quantities.:
We can broadly divide the physical quantities in to two types i)Fundamental Physical quantities ii)Derived physical quantities.
Fundamental physical quantities: A physical quantity which can exist independently is called Fundamental physical quantity.
Ex: Length, mass and time etc.
Derived physical quantities: A physical quantity which can not exist independently is called derived physical quantity. (Or) A physical quantity which is dependent or derived from any other physical quantity is called derived physical quantity.
Ex : Area, volume, density, speed, acceleration, force, energy etc.
Like the physical quantities we can divide the units in to two types. I)Fundamental units ii)derived units.
Fundamental units : The units of fundamental physical quantities are called fundamental units, (or) The units which are independent or can not derived from any other unit is called fundamental unit.
Ex: Every unit of length is fundamental unit (irrespective of the system to which it belongs);millimeter, centimeter, meter, kilometer etc.
Every unit of time is a fundamental unit. microsecond, millisecond, second, minute, hour, day etc are units of time.All these units are fundamental units.
Derived units: The units of derived physical quantities are called derived units. Units of area, volume, speed, density, energy etc are derived units.
Ex: Every unit of speed is a derived unit ; m/sec, cm/sec, km/hr etc.
Every unit of density is a derived unit; kg/m³, gr/cm³ etc.
Every unit of acceleration is a derived unit; m/sec², cm/sec², km/hr² etc.
System of Units: To measure the fundamental physical quantities Length,Mass and Time we have three systems of units, they are i) C.G.S system(metric system) ii) F.P.S system (British system) and iii) M.K.S system. In all these three systems only three physical quantities mass,length and time are considered to be fundamental quantities.
But, in system International (S.I) system there are seven fundamental physical quantities. Which are i)Mass ii)Length iii) Time iv)Electric current v) Thermo dynamic temperature vi) Luminous intensity vii) Quantity of substance.
In addition to the above seven fundamental quantities two more supplementary physical quantities were add.They are i) Plane angle ii)Solid angle.
Filed under: Physics Units Tagged: system of units ]]>
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How to solve problems in Physics.
https://gyaunnrraje.wordpress.com/2010/02/21/howtosolveproblemsinphysics/
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Sun, 21 Feb 2010 09:14:51 +0000
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]]>Many of the students feel Physics as a difficult subject. Because, it involves many calculations, mathematical equations.
To solve the problems in Physics, it is essential to have knowledge of Algebra, Trigonometry, Calculus and integration.
Let me explain few steps to solve problems of physics When a problem is given to you,
# Read the question as many times you want, until you understand it.
# Try to recollect to which branch of the Physics it belongs i.e does it belong to Kinematics or heat or electricity.
# Note down every physical quantity involved in the question, including that physical quantity which has to be calculated in the question, with their symbols Ex: Time as(t); acceleration as (a);mass as (m) .
# Check whether all the physical quantities involved in the question, are in the same system of units C.G.S or F.P.S or S.I system of unit or not.
# If all the physical quantities are not in the same system of units, then convert them in to any one system i.e into either C.G.S or S.I systems of units.
# write an equation relating all the known physical quantities and the physical quantity which has to be determined in the equation.
# Substitute the values of all the physical quantities and constants in the equation.
# Solve the equation for the unknown physical quantity.
# After getting the result write the proper units.
Let me explain with few examples:
Ex 1) A person of mass 50kg in a lift. Calculate the apparent weight of the person when he moves ( i ) up with acceleration of 3 m/sec^{2} ( ii ) moves down with an acceleration of 4 m/sec^{2} ,( g = 10m/sec^{2} ).
Soln: After going through the problem, we can understand that the physical quantities involved in the problem are a)Mass of the person (m) = 50Kg ; b)acceleration of the lift (a) = 3 m/sec^{2}c) acceleration due to gravity (g) = 10m/sec^{2} , d) apparent mass of the person ( R ) =?
Part i) Now assume a formula which is connecting m,a,g and R . When the lift is moving up , R=m(g+a),as all the given physical quantities are in the same system of units i.e s.I system, we can directly substitute value in the above equation.
R = 50(10+3); R=50(13) R =650N.
ii) When the lift is moving down the formula to calculate apparent weight is R = m(ga)
R=50(104); R=50(6) ; R=300N
Ex: 2) A 25kg block is in motion on a rough horizontal surface. A horizontal force of 75N is required to keep the body moving with constant speed. Find coefficient of kinetic friction. (g=10 m/)
Soln: After going through the question, we can understand that the physical quantities in the problem are a) =75N, m=25kg,g=10m/, =?
This is a problem of friction, the formula for coefficient
Of kinetic friction = =
= = 0.3
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Find the volume of the given rectangular glass plate using vernier calipers and screw gauge.
https://gyaunnrraje.wordpress.com/2009/03/11/findthevolumeofthegivenrectangularglassplateusingverniercalipersandscrewgauge/
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Wed, 11 Mar 2009 14:50:10 +0000
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]]>Formulae:
i) Least count of vernier calipers (L.C) = mm,
S = value of 1 Main scale division , N = Number of vernier divisions.
ii ) Total reading = Main scale reading (a) mm + ( n*L.C ) mm
iii) Pitch of the screw =
iv) Least count of Screw gauge (L.C) =
v) Total Reading = P.S.R + ,
P.S.R = Pitch scale reading , n= Corrected Head scale reading , L.C = Least count
vi) Volume of the glass plate V =
l = length of the glass plate, b = breadth of glass plate , h = Thickness of glass plate.
Procedure :First we have to determine the least count count of the given vernier calipers.
From the given vernier calipers
S= Length of Main scale division = 1 mm = 0.1 cm,
N = Number of vernier scale divisions = 10 ,
Substitute these values in the formula of Least count L.C = = =0.01 cm.
Draw neat diagram of Vernier calipers
Part I : To determine the length ( l )and breadth (b) of the given glass plate with vernier calipers :The given glass plate is held between two jaws of vernier calipers, first to measure its length.Note down the values of the Main scale reading (M.S.R ) and vernier coincidence (VC) in TableI, take 3set of readings by placing the glass plate in 3 different positions.Each time calculate the total reading by substituting the values of M.S.R and VC in the formula Total reading = M.S.R + (.
Find the average of 3readings and calculate Average Length ( l )of the given glass plate.
Now hold the glass plate between jaws of vernier calipers breadth wise ,repeat the experiment as above , note down the 3 set of readings of M.S.R and VC in TableII.Calculate average breadth (b) of the glass plate
Part II: To determine thickness(h) of glass plate using Screw gauge:First we have to determine the least count of the given Screw gauge.
Number of complete rotations of the screw = 5
Distance moved by sloped edge over the pitch scale = 5mm
Pitch of the screw = = =1mm.
Number of divisions on the head scale = 100
Least count (L.C) = = =0.01mm
Draw neat diagram of Screw Gauge
Zero Error :Now check whether the given screw gauge has any ZERO ERROR or not. To determine the ZERO ERROR, the head H is rotated until the flat end of the screw touches the plane surface of the stud (do not apply excess pressure) i.e we have to rotate the head only by means of safety device ‘D’ only.
When and are in contact,the zero of the head scale perfectly coincides with the index line as in Fig(a). In such case there will be no ZERO ERROR and no correction is required.
When and are in contact,the zero of the head scale is below the index line as in Fig(b), such ZERO ERROR is called positive ZERO ERROR, and the correction is negative.
When and are in contact,the zero of the head scale is above the index line as in Fig(c) , such ZERO ERROR is called negative ZERO ERROR, and the correction is positive.
When and are in contact,98 th division of head scale is coinciding with index line i.e the zero of the head scale is 3 divisions below the index line as in Fig(b), such ZERO ERROR is called positive ZERO ERROR, and the correction is negative.
The Zero correction for the given screw gauge = – 2
The given glass plate is held between the two parallel surfaces of fix stud and screw tip . Note the completed number of divisions on pitch scale, which is called PITCH SCALE READING (P.S.R). The number of the head scale division coinciding with the index line is noted, which is called OBSERVED HEAD SCALE READING n’. If the given screw gauge has ZERO ERROR (x) the correction is made by adding or subtracting the ZERO ERROR (x) from the OBSERVED HEAD SCALE READING n’.The corrected value (n’x) or (n’+x) is called the HEAD SCALE READING (H.S.R) n.
To calculate the fraction the H.S.R (n) is multiplied by the least count (L.C).
Diameter of first wire = Total reading = P.S.R + – – – – – – (1)
Changing the position of the glass plate, 3 readings should be taken, and recorded in the tableIII. Every time calculate the total thickness (h)of glass plate using equation (1).
Calculate average of 3readings which is average thickness (h) of glass plate.
TableI: Length (l) of the glass plate :
S.No
M.S.R
a cm
Vernier Coincidence (n)
Fraction b=n*L.C
Total Reading (a+b) cm
1
2.5
8
0.01*8=0.08
2.58
2
2.5
9
0.01*9=0.09
2.59
3
2.5
7
0.01*7=0.07
2.57
Average length of glass plate (l) = = = 2.58 cm
Average length of glass plate (l) = 2.58 cm or 25.8mm
TableII: Breadth (b)of the glass plate :
S.No
M.S.R a cm
Vernier Coincidence (n)
Fraction b=n*L.C
Total Reading (a+b) cm
1
1.1
4
0.01*4=0.04
1.14
2
1.1
5
0.01*5=0.05
1.15
3
1.1
5
0.01*5=0.05
1.15
Average Breadth of glass plate (b) = = = 1.15 cm.
Average Breadth of glass plate (b) = 1.15 cm or 11.5 mm.
TableIII: Thickness (h)of the glass plate :
S.No
Pitch Scale Reading (P.S.R) amm
Observed H.S.R (n’)
Correction (x)
Corrected H.S.R n=n’(+/)x
Fraction b=n*L.C
Total reading (a+b) mm
1
2
75
2
752=73
73*0.01=0.73
2.73
2
2
74
2
742=72
72*0.01=0.72
2.72
3
2
76
2
762=74
74*0.01=0.74
2.74
Average Thickness (h) of glass plate (b) = = = 2.73 mm.
Average Thickness of glass plate (h) = 2.73 mm.
Observations :
i)Average length of glass plate (l) = 2.58 cm or 25.8mm
ii)Average Breadth of glass plate (b) = 1.15 cm or 11.5 mm.
iii)Average Thickness of glass plate (h) = 2.73 mm.
Calculations : Volume of the given glass plate V =
Volume of the given glass plate V = =809.99
Precautions :
1) Take the M.S.R and vernier coincide every time without parallax error.
2)Record all the reading in same system preferably in C.G.S system.
3) Do not apply excess pressure on the body held between the jaws.
4) Check for the ZERO error.When the two jaws of the vernier are in contact,if the zero division of the main scale coincides with the zero of the vernier scale no ZERO error will be there.If not ZERO error will be there, apply correction.
5) Pitch scale reading (P.S.R) should be taken carefully without parallax error
6) Head scale reading (H.S.R) should be taken carefully without parallax error
7)Screw must be rotated by holding the safety device ‘D’
8 ) Do not apply excess pressure on the object held between the surfaces and .
Result : Volume of the given glass plate is V= 809.99
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\frac{S}{N}
\frac{Distance moved by sloped edge over the pitch scale}{Number of rotations of the screw}
\frac{Pitch of the screw}{Number of divisions on Head scale}
n\times L.C
\frac{S}{N}
\frac{0.1}{10}
\frac{Distance moved by sloped edge over the pitch scale}{Number of rotations of the screw}
\frac{5mm}{5}
\frac{Pitch of the screw}{Number of divisions on Head scale}
\frac{1mm}{100}
S_2
S_1
zeroerror
S_1
S_2
S_1
S_2
S_1
S_2
S_1
S_2
S_1
S_2
n\times L.C
S_1
S_2

Compare the radii of given three wires using Screw Gauge.
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]]>Formulae :
i ) Pitch of the screw = .
ii ) Least count (L.C) = ,
iii ) Total Reading = P.S.R + ,
P.S.R = Pitch scale reading , n= Corrected Head scale reading , L.C = Least count
iv ) Ratio of radii of the three given wires is ::,
where = Average radius of first wire,
= Average radius of second wire,
= Average radius of third wire.
Procedure :First we have to determine the least count of the given Screw gauge.
To determine the least count of the screw gauge, the head ‘H’ is rotated through certain (say 5) number of complete rotations.The distance moved by the sloped edge over the pitch scale is measured.
Now substitute these values in the formula of pitch of the screw = .
Least count L.C = .
Now check whether the given screw gauge has any ZERO ERROR or not. To determine the ZERO ERROR, the head H is rotated until the flat end of the screw touches the plane surface of the stud (do not apply excess pressure) i.e we have to rotate the head only by means of safety device ‘D’ only.
When and are in contact,the zero of the head scale perfectly coincides with the index line as in Fig(a). In such case there will be no ZERO ERROR and no correction is required.
When and are in contact,the zero of the head scale is below the index line as in Fig(b), such ZERO ERROR is called positive ZERO ERROR, and the correction is negative.
When and are in contact,the zero of the head scale is above the index line as in Fig(c) , such ZERO ERROR is called negative ZERO ERROR, and the correction is positive.
Determine the radii of the given metal wires :The given object metal wire is held between the two parallel surfaces of fix stud and screw tip . Note the completed number of divisions on pitch scale, which is called PITCH SCALE READING (P.S.R). The number of the head scale division coinciding with the index line is noted, which is called OBSERVED HEAD SCALE READING n’. If the given screw gauge has ZERO ERROR (x) the correction is made by adding or subtracting the ZERO ERROR (x) from the OBSERVED HEAD SCALE READING n’.The corrected value (n’x) or (n’+x) is called the HEAD SCALE READING (H.S.R) n.
To calculate the fraction the H.S.R (n) is multiplied by the least count (L.C).
Diameter of first wire = Total reading = P.S.R + – – – – – – (1)
Changing the position of metal wire, 5 readings should be taken, and recorded in the table1. Every time calculate the total diameter (d) of the metal wire using equation (1).
Average of the 5 diameter of the metal wire should be calculated, to get the average diameter(d) of the first metal wire.
Radius () of the first metal wire = mm.
The diameters of 2nd and 3rd wires are also measured following the above procedure. From diameters of 2nd and 3rd wires we can calculate their radii and .
Calculation of least count:
Number of complete rotations of the screw = 5
Distance moved by sloped edge over the pitch scale = 5mm
Pitch of the screw = = =1mm.
Number of divisions on the head scale = 100
Least count (L.C) = = =0.01mm
Zero Error :
When and are in contact,97 th division of head scale is coinciding with index line i.e the zero of the head scale is 3 divisions below the index line as in Fig(b), such ZERO ERROR is called positive ZERO ERROR, and the correction is negative.
The Zero correction for the given screw gauge = – 3
Table 1 ( Diameter of the 1st wire) :
S.No
Pitch Scale Reading (P.S.R) amm
Observed H.S.R (n’)
Correction (x)
Corrected H.S.R n=n’(+/)x
Fraction b=n*L.C
Total reading (a+b) mm
1.
1
45
3
453=42
42*.001=0.42
1.42
2.
1
46
3
463=43
43*0.01=0.43
1.43
3.
1
46
3
463=43
43*0.01=0.43
1.43
4.
1
47
3
473=44
44*.001=0.44
1.44
5.
1
46
3
463=43
43*0.01=0.43
1.43
Average diameter of the 1st wire () = = mm.
Average diameter of the 1st wire () = 1.43 mm
Average radius of 1st wire () = = =0.72 mm
Table – 2 (Diameter of the 2nd wire):
S.No
Pitch Scale Reading (P.S.R) amm
Observed H.S.R (n’)
Correction (x)
Corrected H.S.R n=n’(+/)x
Fraction b=n*L.C
Total reading (a+b) mm
1.
2
12
3
123=9
9*0.01=0.09
2.09
2.
2
13
3
133=10
10*0.01=0.10
2.10
3.
2
14
3
143=11
11*0.01=0.11
2.11
4.
2
12
3
123=9
9*0.01=0.09
2.09
5.
2
14
3
143=11
11*0.01=0.11
2.11
Average diameter of the 1st wire () = = mm.
Average diameter of the 2nd wire () = 2.10 mm
Average radius of 2nd wire () = = =1.05 mm
Table 3 ( Diameter of the 3rd wire) :
S.No
Pitch Scale Reading (P.S.R) amm
Observed H.S.R (n’)
Correction (x)
Corrected H.S.R n=n’(+/)x
Fraction b=n*L.C
Total reading (a+b) mm
1.
1
85
3
853=82
82*0.01=0.82
1.82
2.
1
84
3
843=81
81*0.01=0.81
1.81
3.
1
84
3
843=81
81*0.01=0.81
1.81
4.
1
86
3
863=83
83*0.01=0.83
1.83
5.
1
86
3
863=83
83*0.01=0.83
1.83
Average diameter of the 1st wire () = = mm.
Average diameter of the 3rd wire () = 1.82 mm
Average radius of 1st wire () = = =0.91 mm
Observations : i)Average radius of 1st wire () = 0.72 mm,
ii)Average radius of 2nd wire () = 1.05 mm,
iii )Average radius of 3rd wire () = 0.91 mm.
Precautions : i ) Pitch scale reading (P.S.R) should be taken carefully without parallax error ii ) Head scale reading (H.S.R) should be taken carefully without parallax error iii )Screw must be rotated by holding the safety device ‘D’ iv ) Do not apply excess pressure on the object held between the surfaces and .
v ) The screw is rotated in only one direction either clock wise or anticlock wise to avoid the back lash error.
Result : Ratio of radii of the given wires is :: = 0.72 : 1.05 : 0.91
Posted in Experiments, Screw Gauge Tagged: Measurements, Screw Gauge ]]>
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\frac{Distance moved by sloped edge over the pitch scale}{Number of rotations of the screw}
\frac{Pitch of the screw}{Number of divisions on Head scale}
n\times L.C
\frac{Distance moved by sloped edge over the pitch scale}{Number of rotations of the screw}
\frac{Pitch of the screw}{Number of divisions on Head scale}
S_2
S_1
zeroerror
S_1
S_2
S_1
S_2
S_1
S_2
S_1
S_2
n\times L.C
\frac{Distance moved by sloped edge over the pitch scale}{Number of rotations of the screw}
\frac{Pitch of the screw}{Number of divisions on Head scale}
S_1
S_2
S_1
S_2