A to Z of Physics

2011 in review

gyaunnrraje — Mon, 23 Jan 2012 15:13:37 +0000

The WordPress.com stats helper monkeys prepared a 2011 annual report for this blog.

Here’s an excerpt:

The Louvre Museum has 8.5 million visitors per year. This blog was viewed about 78,000 times in 2011. If it were an exhibit at the Louvre Museum, it would take about 3 days for that many people to see it.

Click here to see the complete report.

Filed under: 5584

Table of Units and Dimensions of Physical quantities.

gyaunnrraje — Sat, 13 Aug 2011 03:37:51 +0000

Units & Dimensions of Physical quantities in S.I system.

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			kg-m/ or Newton
13.	Weight	w=mg		kg-m/ 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) N-sec/$latex \m^2$ (or)pascal-sec (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 (Ω-m)
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.	Co-efficient 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

Filed under: Physics Dimensions Tagged: Dimensional formula, Formula's, Units, Units & Dimensions of Physical

Vector operations:

gyaunnrraje — Fri, 24 Jun 2011 18:08:16 +0000

Addition of vectors: If two scalars are added resulting scalar will be unique which will be equal to sum of the given two scalars.For examples if two scalars 2 and 8 are added their sum will be always equal to 2+8 =10.

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 – –

Filed under: Vectors Tagged: Vecor subtraction, Vector addition

HTML codes

gyaunnrraje — Sun, 29 May 2011 07:02:37 +0000

{(X+Y+Z)
(A+B+C)}⁵is an expression.the eapansion of this expression contains 10 terms.X₂

C.R.MARKETING	4-8-90/3/1	NEAR SBM GARDENS	MANJEERA NAGAR	SANGAREDDY	DIST:MEDAK
C.R.ENTERPRISES	4-8-90/3/1	NEAR SBM GARDENS	MANJEERA NAGAR	SANGAREDDY	DIST:MEDAK

vrd

srd

dgi



Filed under: 5584



VECTORS
gyaunnrraje — Tue, 17 May 2011 15:29:40 +0000
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.Co-initial 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 co-initial vectors.
2.Co-terminal 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 co-terminal vectors.
3. Coplanar Vectors:The vectors which lie in the same plane  are called Co-planar  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 co-ordinate 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.
 The given vectors  and 
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 X-axis. 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 X-axis or parallel to X-axis in positive direction. ii) 8/5   is a vector of 8/5 units magnitude working along X-axis or parallel to X-axis in positive direction. iii) -9  is a vector of 9units magnitude working along X-axis or parallel to X-axis in negative direction. iv)a  is a vector of a units magnitude working along X-axis or parallel to X-axis 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 Y-axis. 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 Y-axis or parallel to Y-axis in positive direction. ii) 5/3   is a vector of 5/3units magnitude working along Y-axis or parallel to Y-axis in positive direction. iii) -7  is a vector of 7units magnitude working along Y-axis or parallel to Y-axis in negative direction. iv)b  is a vector of b units magnitude working along Y-axis or parallel to Y-axis 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 Z-axis. 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 Z-axis or parallel to Z-axis in positive direction. ii) 8/5   is a vector of 8/5 units magnitude working along Z-axis or parallel to Z-axis in positive direction. iii) -4  is a vector of 4units magnitude working along Z-axis or parallel to Z-axis in negative direction. iv)c  is a vector of c units magnitude working along Z-axis or parallel to Z-axis in positive direction.
10.Two dimensional vectors (or) Plane vectors:The vectors acting in XY-Plane or YZ-Plane or ZX-Plane are known as two dimensional vectors or also known as vectors in a plane.
10(i).Vectors in XY-Plane: In the given Fig(i)  =  is a vector working in XY-Plane.It’s X-component 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 XY-Plane will have only two components X-component and Y-component.These XY-plane vectors can also be represented in Cartesian co-ordinate form.  =( ,  , 0).
Note: If X,Y co-ordinates exists(not equal to zero) and the Z co-ordinates does not exist(=0), such vectors will be in XY plane.
10(ii).Vectors in YZ-Plane:  In the given Fig(ii)  =  is a vector working in YZ-Plane.It’s Y-component 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 YZ-Plane will have only two components Y-component and Z-component.These YZ-plane vectors can also be represented in Cartesian co-ordinate form.  =(0, ,  ).
Note: If Y,Z co-ordinates exists(not equal to zero) and the X co-ordinates does not exist(=0), such vectors will be in YZ plane.
10(iii).Vectors in XZ-Plane: 
In the given Fig(i)  =  is a vector working in XZ-Plane.It’s X-component 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 XZ-Plane will have only two components X-component and Z-component.These XZ-plane vectors can also be represented in Cartesian co-ordinate form.  =( ,0,  ).
Note: If X,Z co-ordinates exists(not equal to zero) and the Y co-ordinates 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 co-ordinate form.  =( ,,  ).
In the given fig  is a space vector .Where OC =   , OA =  and OG = .Hence  =   =    +   +   .

Filed under: Vectors Tagged: Types of vectors        


Physics in Every Day Life
gyaunnrraje — Sun, 15 May 2011 16:15:13 +0000
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)         


Types of Units
gyaunnrraje — Sun, 04 Apr 2010 17:07:40 +0000
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        


How to solve problems in Physics.
gyaunnrraje — Sun, 21 Feb 2010 09:14:51 +0000
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/sec² ( ii ) moves down with an acceleration of 4 m/sec² ,( g = 10m/sec² ).
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/sec²c) acceleration due to gravity (g) = 10m/sec² , 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(g-a)
R=50(10-4); 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 co-efficient
Of kinetic friction = =
= = 0.3

Filed under: GENERAL         


Find the  volume of the given rectangular glass plate using vernier calipers and screw gauge.
gyaunnrraje — Wed, 11 Mar 2009 14:50:10 +0000
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 Table-I, 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 Table-II.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 table-III. 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.
Table-I: 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
Table-II: 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.
Table-III: 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
75-2=73
73*0.01=0.73
2.73


2
2
74
2
74-2=72
72*0.01=0.72
2.72


3
2
76
2
76-2=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 

Posted in Experiments, Screw Gauge Tagged: Question & answers, Screw Gauge        


Compare the radii of given three wires using Screw Gauge.
gyaunnrraje — Wed, 04 Mar 2009 17:30:38 +0000
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.
Draw figure
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 table-1. 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
45-3=42
42*.001=0.42
1.42


2.
1
46
3
46-3=43
43*0.01=0.43
1.43


3.
1
46
3
46-3=43
43*0.01=0.43
1.43


4.
1
47
3
47-3=44
44*.001=0.44
1.44


5.
1
46
3
46-3=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
12-3=9
9*0.01=0.09
2.09


2.
2
13
3
13-3=10
10*0.01=0.10
2.10


3.
2
14
3
14-3=11
11*0.01=0.11
2.11


4.
2
12
3
12-3=9
9*0.01=0.09
2.09


5.
2
14
3
14-3=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
85-3=82
82*0.01=0.82
1.82


2.
1
84
3
84-3=81
81*0.01=0.81
1.81


3.
1
84
3
84-3=81
81*0.01=0.81
1.81


4.
1
86
3
86-3=83
83*0.01=0.83
1.83


5.
1
86
3
86-3=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  anti-clock 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

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

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

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	75-2=73	73*0.01=0.73	2.73
2	2	74	2	74-2=72	72*0.01=0.72	2.72
3	2	76	2	76-2=74	74*0.01=0.74	2.74