Government Polytechnic Muzaffarpur

Name of the Lab: Applied Science Lab

Subject Code: 1602107

EXPERIMENT NO.1

Practical Name: Spring constant

Aim: to determine the force constant or spring constant (stiffness constant k) by using oscillation

method.

Apparatus and material required: A light weight helical spring with a pointer attached at the lower

end and a hook, A rigid support, hanger and five slotted weight of 10 gram Clamp stand, A

measuring scale and Stop watch.

Principle:

Spring constant or force constant of a spring is given by

Spring constant, K= 𝑅𝑒𝑠𝑡𝑜𝑟𝑖𝑛𝑔 𝑓𝑜𝑟𝑐𝑒

𝐸𝑥𝑡𝑒𝑛𝑠𝑖𝑜𝑛

(1) Thus, spring constant is the restoring force per unit extension in the spring. Its value is

determined by the elastic property of the spring. A given object is attached to the free end of a

spring which is suspended from a rigid point support (a nail, fixed to a wall). If the object is pull

down and the released, it executes simple harmonic oscillation.

The relationship between time period (T) and spring constant is given by

T= 2𝜋√𝑚

𝑘 Where m is the load of the object. If spring

has large mass itself then expression change to

T= 2𝜋 (𝑚𝑜+𝑚

𝑘) 1/2 (2)

Where mo. and m are the effective masses of the spring system.

One can easily eliminate the term m0 of the spring system appearing in

equation (2) by substituting two different object (load) of masses m1 and

m2 and measuring their respective period of oscillation T1 and T2 .Then

T1= 2𝜋(𝑚𝑜+𝑚1

𝐾)1/2 (3)

And T2 =2𝜋(𝑚𝑜+𝑚2

𝐾)1/2 (4)

Eliminate the term mo. from equation and above equation and subtract the

equation 4 from 3, we get

K = 4𝜋2(m1-m2) / (T12-T2

2) (5)

Using equation (5) we can calculate the value of spring constant

1. Suspend the helical spring SA (having pointer P and the hanger H at its free end A),

from a rigid support, as shown in figure (1).

2. Set the measuring scale, close to the spring vertically. Take care that the pointer P

moves freely over the scale without touching it.

3. Suspended the load or slotted weight with mass m1 on the hanger gently. Wait till the

pointer comes to rest. This is the equilibrium position for the given load. Pull the load

slightly downwards and then release it gently so that it is set into oscillation in a

vertical plane about its rest (or equilibrium) position. The rest position (X) of the

pointer P on the scale is the reference or mean position for the given load. Start the

Stop watch as the pointer P just crosses its mean position (say, upward to downwards)

and simultaneously being to count the oscillations.

4. Keep on counting the oscillation as the pointer crosses the mean position (x) in the

same direction. Stop the watch after n (say, 10to 2o) oscillation are complete. Note

the time (t) taken by the oscillating load for n oscillations.

5. Repeat this observation at least thrice and in each occasion note the time taken for

the same number of oscillation (n). Find the mean time (t1), for n oscillation and

compute the time for one oscillation, i.e., the time period T1 (=t1/n) of oscillating

helical spring with load m1.

6. Repeat steps 3 and 4 for two more slotted weights.

7. Calculate time period of oscillation T=t/n for each weight and tabulate your

observations.

8. Compute the value of spring constant (K1, K2 and K3) for each load and find out the

mean value of spring constant K of the given helical spring.

Observation:

Least count of the measuring scale = ….. mm = ……cm.

Least count of the stop watch = …..s

Mass of load m1 = ……g = …..Kg

Mass of load m2 =…….g =……kg

Mass of the load m3 =….g = …….kg

Table: Measuring the time period T of oscillation of helical spring with load.

S.

No.

Mass of the load m

(kg)

Mean

position of

the pointer.

X in cm

No. of

oscillation. n

Time for n

oscillation. t (s)

Time

period. T=

t/n (s)

1 2 3 Mean

Substitute the value of m1, m2, m3 and T1, T2, T3 in above equation. We get

K1=4𝜋2(m1-m2) / (T12-T22);

K2= 4𝝿2 (m2-m3) / (T22-T3

2);

K3 = 4𝝿2 (m1-m3) / (T12-T2

2);

Compute the value of k1, k2, and K3 and find the mean value of spring constant K of the given

helical spring. Express the result in proper SI unit sand significant figure.

Result: thus spring constant of the given helical springs …….N/m.

Precaution:

1. The spring should be suspended freely from a rigid support.

2. Loading of weight must be done gently.

3. Reading should be noted only when tip of the pointer comes to rest.

4. Pointer tip should not touch the scale surface.

5. Loading should note be beyond the elastic limit.

Government Polytechnic Muzaffarpur

Name of the Lab: Applied science lab

Subject Code: 1602107

EXPERIMENT NO. 2

Practical Name: Determination of (g)

Aim: To determine the value of acceleration due to gravity (g) with the help of bar

or compound pendulum.

Apparatus used: Bar pendulum, stop watch, Knife edges fixed to rigid support,

Telescope and Meter scale.

Theory: This experiment is based on the interchange ability of the centers of

sustention and oscillation. The distance between center of sustention and center of

oscillation is known as "length of equivalent simple pendulum".

L= 𝑲𝟐

𝒍+ 𝒍 Knowing this value, ‘g’ can be calculated.

The relation between time period and acceleration due to gravity is given by

T=2𝜋√𝐿/𝑔 (1)

g= 4𝜋2𝐿

𝑇2 (2)

Where T= time period of oscillation.

L= Distance between center of oscillation and suspension.

Description: A bar pendulum consist of uniform rectangular bar AB about one

meter (100cm) long and 2cm in breath, with holes drilled along its length at equal

distance from each other. The lies on the straight line passing through the center

of gravity of the pendulum. A sharp knife edge is attached to some heavy frame

provided with leveling screw s1, s2 and s3 to make the knife edge horizontal. The

bar can be suspended from any holes with the help of knife edge.

Procedure:

1. The bar pendulum is suspended vertically about the knife edge from the

hole nearest to one end.

2. The knife edge is made horizontal by means of levelling screws.

3. A telescope is focused on the lower end of the pendulum. The bar is

allowed to oscillate through small angle with knife edge passing through

the hole no (1) and the time for 30 oscillation is noted with the help of stop

watch. The time period of thirty oscillation is calculated.

4. Then the bar pendulum is suspended successively from its other hole and

the corresponding time for 30 oscillation is noted. This distance of each

hole from any one end of the bar pendulum is also noted. Further the

position of C.G, is determined by balancing the pendulum about a knife

edge.

5. A graph is plotted between the measured distance and the corresponding

time period.

Observation table:

No. of

holes

Distance of the

knife edge from

the end A

No. of

oscillation

Time taken in (s) Time period

1 2 3 mean

Result: From graph

PR= …….. cm= ……. m

QS= ………cm=………m

OE = T = ……. S.

g = 4π2 (𝐿

𝑇2) = …….m/s2.

Sources of error and Precaution:

1. The knife edge is made horizontal before starting the experiment.

2. The amplitude of oscillation should be kept small.

3. The time of oscillation should be counted at least for 30 oscillation with

the help of telescope.

4. The pendulum should be oscillate only in a vertical plane.

5. Smooth curves should be drawn on the graph paper.

Government Polytechnic Muzaffarpur

Name of the Lab: Applied science lab

Subject Code: 1602107

EXPERIMENT NO. 3

Practical Name: Speed of sound

Aim: to find the speed of sound in air at room temperature using a resonance tube apparatus

by two position method.

Apparatus:

1. Resonance tube apparatus

2. Two tuning fork of different frequencies

3. A rubber pad

4. Water in a beaker.

5. A plumb line.

6. A thermometer.

7. A set-square.

Theory: if l1 and l2 are the length of the air column for first and second resonance

position as shown in figure (3).

Then l1 + x = λ/4 (1).

l2 + x = λ/4 (2).

Where x is the end- correction and λ is the wave length of the sound wave.

From (1) and (2) we have

l2 –l1= λ/2 (3).

Or λ = 2(l2-l1) (4).

Let v is the velocity of sound and n is the frequency, then

V = n λ

From equation (3) and (4), we get, v= 2n (l2-l1) (5).

Procedure:

1. Set the resonance tube apparatus vertically with the help of plumb line and by

adjusting the leveling screw S-S provided with the base of the apparatus.

2. Note the room temperature with the help of the thermometer and fill some portion

of resonance tube and reservoir with water.

3. Open the pinch cock P and adjust the level of water in the resonance tube near the

end A by adjusting the position of the reservoir R and then close the pinch cock.

Now lower down the reservoir, keeping the pinch cock tight.

4. Strike the tuning fork gently on the rubber pad and place it just above the open end

A of the resonance tube in such a manner so that it prongs are in vertical plane.

Open the pinch cock and allow the water level to fall gradually till the intensity of

the sound heard maximum. At this position close the pinch cock at once and note

the position of the water level with the help of set- square keeping one of its

perpendicular edges tangential to meniscus of the water and other edge parallel to

the line of graduation on the meter scale. Record this reading of first resonance

length l1 when the water level is falling.

5. Now lower the water level in resonance tube by a few cm, close the pinch cock and

rise the reservoir to the highest position. Now place the vibrating tuning fork over

the open end of tube and release the pinch cock. Allow the water in the tube to rise

slowly till the intensity of sound heard maximum. Note this position of water level

with the help of set-square and record this reading of first resonating length l1 when

the water level is rising.

6. Find the first resonant length of air column with the same tuning fork for two times

more and hence find the mean first resonant length l1.

7. To find the second resonant length l2 with the same tuning fork, lower the position

of water level so that the length of air column is increased about three times the

length l1. Repeat the steps3, 4, 5and 6to get the second position of resonance with

the same tuning fork. Record this length l2 of the air column.

8. Now take the second tuning fork and repeat the steps 3,4,5,6 and 7.

9. Note the room temperature with the help of thermometer.

10. Record all the observation in the table.

Observations:

Room temperature in the beginning of the experiment t1 = t1=…….C0.

Room temperature at the end of the experiment = t2 = …..C0.

Frequency of the first tuning fork = ….Hz.

Frequency of the second tuning fork = …..Hz.

Reading of the upper end (open end) A of the resonance tube = a = ……cm.

Table for the calculation of the resonant length l1and l2.

Frequency of tuning fork(Hz)

Resonance S. No.

Position of water at resonance (b)

Mean resonant length of air column(b-a) cm

Water level falling(cm)

Water level rising(cm)

Mean(b)

n1 First 1 2

l1

Second 1 2

l2

n2 First 1 2

l1

Second 1 2

l2

Calculate the velocity of sound v1 in air by putting the value of n1, l1 and l2 in the

formula

V1 = 2n1 (l2-l1)

= ……m/s.

In the same manner, calculate the velocity of in air v2 by putting the value of n1, l1 and l2

in the formula

V2 = 2n2 (l2-l1)

= ….. M/s.

Mean value velocity of sound at room temperature = v1+v2/2

V t = ….. M/s.

Result: Velocity of sound in air at room temperature (t = c) using a resonance

tube by two resonance position method is ….m/s.

Precaution:

The resonance tube apparatus should be placed vertically.

The tuning fork should be strike gently on the rubber pad.

The vibrating tuning fork should be held horizontally over the open end of the tube.

The prongs of vibrating tuning fork should note touch the tube.

Sources of error:

The resonance tube may not be vertical.

The pinch cock may be loose.

The presences of moister in the tube will be increase the velocity of sound.

Government Polytechnic Muzaffarpur

Name of the Lab: Applied Science Lab

Subject Code: 1602107

EXPERIMENT NO.4

Practical Name: sonometer

Aim: To determine the frequency of sound using sonometer.

Apparatus:

1. A sonometer 2. A set of tuning forks of known frequency.

3. 0.5kg weight hanger.

4. Some 0.5kg slotted weights.

5. Rubber pad.

6. Paper rider.

7. Meter scale.

Theory: when a stretched wire is set in vibrations, the frequency n of the

fundamental note is produced by it, is given by

n = 1/2l √ ……… (1)

Where l is the length of the vibrating wire.

T is the tension in the wire.

m is the mass per unit length of the wire.

For a give wire, m (mass per unit length) is constant, and wire is stretched under

given tension i.e., T is constant, i.e., if m and T are kept constant then equation

(1) gives

n 1/l or n l = constant

Hence if we plot a graph between n and 1/l the graph will be a straight line.

To find the relation between frequency and length

1. Place the sonometer on the table.

2. Make sure that the pulley is frictionless. If you feel any friction, oil them.

3. Stretch the wire by placing a suitable maximum load on the weight hanger.

4. Move the wooden bridges outward, so that the length of wire between the

bridges is maximum.

5. Take a tuning fork of known frequency. Make it vibrate by strike its prong

with a rubber pad. Bring it near the ear.

6. Pluck the sonometer wire and leave it to vibrate.

7. Compare the sounds produced by tuning fork and sonometer wire. (Sound

which has low pitch has less frequency).

8. Gently adjust the bridges for decreasing the length of wire, till the two

sounds appear alike.

9. Put an inverted V shaped paper rider on the middle of the wire.

10. Vibrate the tuning fork and touch the lower end of its handle with sonometer

board. The wire vibrates due to resonance and the paper rider falls.

11. Measure the length of wire between the bridges using a meter scale. It is the

resonant length and record it in the ‘length decreasing’ column.

12. Now, bring the bridges closer and then slowly increase the length of the wire

till the paper rider falls.

13. Measure the length of wire and record it in ‘length increasing’ column.

14. Repeat the above steps with tuning forks of other frequencies, and find

resonant length each time.

To find the relation between length and tension

1. Select a tuning fork of known frequency

2. Set the load in the weight hanger as maximum.

3. Repeat the steps in the previous section to find out the resonant length.

4. Now, remove 0.5kg weight from the weight hanger and find resonant length

with same tuning fork.

5. Repeat the experiment by removing slotted weights one by one in equal

steps of 0.5kg.

6. Record the observations each time.

1. Change the position of bridge A using the slider.

2. Change the position of bridge B using the slider.

3. Click on the ‘Place the paper rider’ button to place the paper rider back.

4. To redo the experiment, click on the ‘Reset’ button.

Observations:

Constant value of load on the wire = M kg

Constant value of tension on the wire= T = …..N

Table for the calculation of frequency and resonant length

S l

No.

Frequency of

tuning fork

used, f (Hz)

Resonant length of wire 1/ l

(cm-1) Length

increasing

l1(cm)

Length

decreasing

l2 (cm)

Mean l = (l1 +l2)

/ 2

Calculations:

1. Plot a graph between 1/l and frequency n of the tuning fork, taking n along

X-axis and 1/l along Y- axis. It will be a straight line as shown in figure.

2. The product of n × l = constant for all the observation within the

experimental error.

Result: The frequency V/s reciprocal of length graph is a straight line, which

indicates that, frequency is inversely proportional to resonant length.

Observation:

Constant frequency of tuning fork = n = ……Hz.

Table for the calculation of resonant length and tension in the wire

S l

No.

Load, M

(kg)

Tension,

T=Mg

(N)

Resonant length of wire l 2

(cm2)

l 2 / T

(cm2/

N)

Length

increasing

l1(cm)

Length

decreasing

l2(cm)

Mean l

= (l1+l2) / 2

Mean, l2 / T =.................. cm2 / N

Find square of resonant length (l2) each time.

Calculate corresponding l2/T value.

Plot a graph between square of length and tension, taking tension along X

axis and square of length along Y axis.

Results

From the tabular column, it is found that; l2/T is a constant. The graph between

square of length and tension is a straight line, which shows that tension is

directly proportional to square of resonant length.

Precaution:

1. The wire should be free from kinks and it should have uniform area of cross-

section.

2. The fully should be frictionless.

3. The wire should not be loaded beyond the elastic limit.

4. The paper rider should be always kept in middle of the wire between the

bridges.

5. While finding the resonant length, start with a small distance between the

bridges.

6. The stem of the tuning fork should be placed gently on the top of the

sonometer box.

7. The weight of the hanger should be counted for the calculation of tension on

the string.

Sources of error:

1. Wire may not have uniform area of cross section.

2. Pulley may not be frictionless.

3. Weight used may not be standard.

4. Bridges may not be sharp.

Government Polytechnic Muzaffarpur

Name of the Lab: Applied science lab

Subject Code: 1602107

EXPERIMENT NO. 5

Practical Name: Determination of refractive index using

spectrometer device.

Aim: To calculate the refractive index of material of prism by using a spectrometer device.

Refractive index μ of the prism is given by the following formula:

Apparatus Required: Spectrometer, prism, mercury vapor lamp, spirit level and reading lens

Where A = angle of the prism, δm = angle of minimum deviation.

Formula Used: Then μ = ( )

(

)

Where A = angle of the prism, δm = angle of minimum deviation.

Procedure: The following initial adjustments of the spectrometer are made first. • The spectrometer and the prism table are arranged in horizontal position by using the

leveling Screws. • The telescope is turned towards a distant object to receive a clear and sharp image. • The slit is illuminated by a mercury vapour lamp and the slit and the collimator are suitably

Adjusted to receive a narrow, vertical image of the slit. • The telescope is turned to receive the direct ray, so that the vertical slit coincides with the

Vertical crosswire.

(A) Measurement of the angle of the prism:

• The telescope is turned to receive the direct ray, so that the vertical slit coincides with the

Vertical crosswire.

• Determine the least count of the spectrometer.

• Place the prism on the prism table with its refracting angle A towards the collimator and with

It’s refracting edge A at the center. In this case some of the light falling on each face will be

Reflected and can be received with the help of the telescope.

• The telescope is moved to one side to receive the light reflected from the face AB and the cross

Wires are focused on the image of the slit. The readings of the two Vernier’s are taken.

• The telescope is moved in other side to receive the light reflected from the face AC and again

the

Cross wires are focused on the image of the slit. The readings of the two Vernier’s are taken.

• The angle through which the telescope is moved; or the difference in the two positions gives

Twice of the refracting angle A of the prism. Therefore half of this angle gives the refracting

Angle of the prism.

(B) Measurement of the angle of minimum deviations:

• Place the prism so that its center coincides with the center of the prism table and light falls on

One of the polished faces and emerges out of the other polished face, after refraction. In this

Position the spectrum of light is obtained.

• The spectrum is seen through the telescope and the telescope is adjusted for minimum

Deviation position for a particular color (wavelength) in the following way: Set up telescope at

a particular color and rotate the prism table in one direction, of course the telescope should be

Moved in such a way to keep the spectral line in view. By doing so a position will come where

a

Spectral line recede in opposite direction although the rotation of the table is continued in the

Same direction. The particular position where the spectral line begins to recede in opposite

Direction is the minimum deviation position for that colour. Note the readings of two

Vernier’s.

• Remove the prism table and bring the telescope in the line of the collimator. See the slit directly

Through telescope and coincide the image of slit with vertical crosswire. Note the readings of

The two Vernier’s.

• The difference in minimum deviation position and direct position gives the angle of minimum

Deviation for that color.

• The same procedure is repeated to obtain the angles of minimum deviation for the other colors.

Figure: Left: Arrangement to determine the angle of prim.

Right: Arrangement to determine the angle of minimum deviation.

Observations:

(i) Value of the one division of the main scale = ……… degrees

Total number of Vernier divisions = ……….

Least count of the Vernier = ………. degrees = ……… second

(ii) Table for the angle (A) of the prism.

S.NO

.

Vernier Telescope reading for reflection Differe

nce

θ = a-

b= 2A

Mean

value

of 2a

A Mean

A

degras From first face From second face

MS

R

VSR T(a) MS

R

VS

R

T(b)

1

V1

V2

2 V1

V2

3 V1

V2

MSR = Main Scale Reading, VSR = Vernier Scale Reading, TR = MSR+VSR = Total Reading.

(iii) Table for the angle of minimum deviation (δm).

S.

No.

Color Vernier Telescope reading

for minimum

deviation

Telescope reading

for direct image

Difference

δm = a – b

Mean

value

of δm

MSR VSR TR

(a)

MSR VSR TR

(b)

1 Violet V1

V2

2 Yellow V1

V2

3 Red V1

V2

MSR = Main Scale Reading, VSR = Vernier Scale Reading, TR = MSR+VSR = Total Reading.

S.

No

Colour Calculated refractive index Standard refractive index % Error

Calculations:

Angle of the prism = ………

Angle of minimum deviation for violet = ………..

Refractive index for violet = …………..

Angle of minimum deviation for blue = …………..

Refractive index for yellow = ………….

Angle of minimum deviation for red = ………..

Refractive index for red = …………..

Result: Refractive index for the material of the prism:

Precautions and sources of error:

(I) The telescope and collimator should be individually set for parallel rays.

(ii) Slit should be as narrow as possible.

(iii)While taking observations, the telescope and prism table should be clamped with the help of

Clamping screws.

(iv)Both Verniers’ should be read.

(v) The prism should be properly placed on the prism table for the measurement of angle of the

Prism as well as for the angle of minimum deviation.

Government Polytechnic Muzaffarpur

Name of the Lab: Basic Physics lab

Subject Code: 1601107

EXPERIMENT NO. 1

Practical Name: VERNIER CALLIPERS

Aim: To Measure The Diameter Of A Small Spherical /Cylindrical Body And

To Measure Internal Diameter And Depth Of A Given Beaker/Calorimeter Using

Vernier Caliper And Hence Find Its Volume.

Apparatus: Vernier Calipers, Spherical body, a beaker or Calorimeter

Theory: When The Body Is Placed Between The Two Jaws A And B ,The

Main Scale Reading Is X And If N Is The Number Of Vernier Scale Division

Coinciding, Then The Observed Reading Is Give As

Observed Reading=X +N (V .C.)

Volume of the Cylinder=V= πr2h

Where D =Diameter of the Cylinder

Procedure: Measurement of diameter of a cylinder or sphere:

We Have First Determine the Vernier Constant (V.C.) Of the Vernier Calipers.

Bring the movable Jaw BD in Close Contact with the Fixed Jaw Ac and Determine the Zero

Error .Take At least Three Reading .Record The Zero Error .If There Is No Zero Error Then

Record Zero Error Nil.

Place The Sphere Or Cylinder R Between The Two Jaws AC And BD , And Adjust The

Jaw BD So That It Gently Grip The Body Between The Two Jaws. Now Tight The Screw S

Attached To The Vernier Scale V.

Take The Main Scale Reading ,I.E., Note The Position Of Zero Mark Of The Vernier Scale

V On Main Scale .For This The Main Scale Reading Just Before The Zero Mark Of The

Vernier Scale. This Reading X Is Called Main Scale Reading (M.S.R).

Note The Number Of Vernier Scale Division(N) Which Coincides With Some Division Of

The Main Scale .The Coinciding Number Is To Be Counted From The Zero End Of Vernier

Scale.

Find The Product of N and V.C. (Y) Which Is Called Vernier Scale Reading (V.S.R).Add

V.S.R. And M.S.R. To obtain Diameter of the Sphere or Cylindrical Object.

Repeat The Observation for the Diameter At Least Three Times, At Three Different Position

of the Sphere or Cylinder .Record The Observation in the Table.

To obtain The Corrected Diameter, Subtract the Zero Error Algebraically from the Observed

Diameter.

Measurement of internal diameter:

Insert The Jaws P and Q (Fig.1) In the Interior of Calorimeter and Adjust the Position of

Moveable Jaws So That P and Q Touch the Walls of the Calorimeter Gently .Tight The Screw S

Attached to the Vernier Scale.

Note The Position Of The Zero Of The Vernier Scale On The Main Scale. This Reading Is

Called Main Scale Reading(X).

Note The Number Of Vernier Scale Division (N) Which Is Coinciding With Some Division

Of The Main Scale.

Repeat The Observation For Internal Diameter Three Times By Changing The Position Of

The Calorimeter And Record The Observation S.

Find The Corrected Mean value Of Internal Diameter by Appling Zero Error.

Measurement Of Depth:

To Measure The Depth Of The Calorimeters N, Use Strip N Of The Vernier Caliper S.

Keep The Edge Of Main Scale Of Vernier Calipers On The Upper Edge Of The Calorimeter

So That Strip N Is Able To Go Inside The Calorimeter Along Its Length As Shown In Fig1.

Now Move The Sliding Jaw Till The Length Of The Strip N Touches The Bottom of The

Calorimeter Gently.

Observation:

10V.S.D. = 9 M.S.D. Or 1V.S.D. = 9

10 M.S.D.

Vernier constant (V.C. /L.C.) = 1M.S.D. – 1V.S.D. = 1M.S.D. - 9

10 M.S.D.

V.C/ L.C. = (1- 9/10) 1M.S.D. = 1/10 × 1M.S.D. = 1/10 ×1mm = 0.1m

V.C. /L.C. = 0.1/10 = 0.01 cm

Table for calculation of diameter

Observation for

Main scale reading (x) cm

No. of Vernier division coinciding(n)

Vernier scale reading y= n × (v.c.) cm

Observed diameter = x + y cm

Mean observed diameter D0 cm

Mean corrected diameter D = D0 + (-e) cm

Diameter Ι Diameter ǁ Diameter ΙΙΙ

1 2 1 2 1 2

D1 = D2 = D3 =

Table for the calculation for internal diameter

S. No. Main scale reading(x) cm

No. of Vernier division coinciding (n)

Vernier scale reading y = n × L.C. cm

Observed internal diameter D0 = x + y cm

Corrected internal diameter Di = d0 +(-e) cm

Table for calculation of depth (h) of calorimeter

S. No. Main scale reading(x) cm

No. of Vernier division (n)

Vernier scale reading y= n × L.C. cm

Observed depth h0 = x+y cm

Corrected depth h = h0 +(-e) cm

Calculation:

Mean Corrected Diameter Of Cylinder=D=D1+D2+D3/ 3=……..Cm

Mean Corrected Internal Diameter D=D1+D2+D3+D4 / 4=………Cm

Mean Corrected Height H=H1+H2+H3+H4 / 4= ………..Cm

Volume Of The Cylinder(V)=𝜋𝑟2H …………….Cm

Result:

He Internal Diameter Of Given Cylinder Is………Cm

The Depth Of Calorimeter Is………Cm

The Volume Of The Given Cylinder Is …….Cm

Precaution:

1. Jaws of the Vernier Calipers Should Note Be pressed Hard.

2. The Vernier Constant And Zero Error Should Be Carefully Calculated And Recorded.

3. The Motion of Vernier Caliper on Main Scale Should Be Smooth. If Not It Should Be

Oiled.

Sources of error:

1. Jaws of the calipers may not be at right angle to the main scale.

2. Vernier scale may be loosely fitted with the movable jaws.

3. The graduations on scale may not be correct and clear.

4. Parallax may be there in taking in observation.

Government Polytechnic Muzaffarpur

Name of the Lab: Basic Physics lab

Subject Code: 1601107

EXPERIMENT NO. 2

AIM: To measure diameter of a give wire and thickness of a of a sheet using screw gauge.

APPARATUS: Screw gauge, Wire, Meter scale, Sheet.

THEORY: If a wire or a sheet is placed between A and B of the cap lies ahead of x division on

pitch scale, then linear scale or pitch scale reading=x

If nth division of circular scale coincides with reference line, then

Circular scale reading=n× L.C.

Observed diameter of wire or thickness of the sheet=x+ n × 𝐿. 𝐶.

Corrected diameter or thickness of the sheet=observed diameter _ zero error

Procedure: (a) measurement of diameter of the wire

1. First of all find the pitch and list count of the given screw gauge.

2. Determine the zero error with proper sign. Repeat it three times and record them. If there

is no zero error, then record zero error nil.

3. Now insert the wire between the screw and stud A. Move the screw forward by rotating

the ratchet till the wire is gently gripped between A and B as shown in figure. Stop

rotating ratchet when ratchet slips without moving the screw.

4. Note the number of division of the linear scale visible and uncovered by the edge of the

cap. The reading x is called linear scale reading.

5. Note which number of division on circular scale (n) is coinciding with the reference line

.The product of n and L. c. gives the circular scale reading.

6. Now release the wire gently from the by loosening the screw. Rotate the wire through 90°

at the same cross-section position. Repeat the step 3 to 5 and take the observed diameter

in perpendicular direction.

7. Repeat the above steps 3to 6 for three different position of the wire.

8. Take the mean of these observed diameters.

9. Apply the zero error correction with proper sign to mean observed diameter and find the

corrected diameter.

(b) Measurement of thickness of the sheet

1. Now insert the given sheet between the screw and stud A. Move the screw forward

by rotating the ratchet till the sheet is gently gripped between A and B as shown in

fig2.Stop to move ratchet when ratchet slips without moving the screw.

2. Note the number of division of the linear scale visible and uncovered by the edge of

the cap.

3. Note which number of division on circular scale (n) is coinciding with the

reference line. The product of n and L.C. gives the circular scale reading.

4. Repeat the step 1, 2 and 3 for four different position throughout the surface of the

sheet. Record observation in tabular form.

5. Take the mean of the observed thickness of the sheet.

6. Apply zero correction with proper sign to mean observed thickness to get corrected

thickness.

Observation:

Determination of least count of screw gauge

Let number of complete rotation given to the circular scale = a =……

Distance moved by the screw = b =…….mm

Pitch=b ÷a=…mm

Total number of division on circular scale =N=…….

Least count = pitch / N=……mm

ZERO ERROR

(1) ……….mm (2) …….mm (3) ……..mm

Mean zero error=e=………mm

Mean zero error correction= (-e) = ……mm

Mean observed diameter =d0 = d’1+d’2+d’3 +d’4/ 4 = ……..mm

Mean corrected diameter = d = d0+ (-e) = ………. mm

RESULT:

1. The diameter of given wire is ………cm.

2. The thickness of given sheet is ………cm.

PREACUTION:

1. The screw should free from friction. It should be oiled if it is needed.

2. Screw should be always turned by ratchet and not by cap to avoid excess pressure.

3. Zero correction must be noted with proper sign and added algebraically.

4. Stop turning the ratchet, when it start slipping.

5. Take the reading of the diameter in two mutually perpendicular directions.

6. Error due to the parallax should be avoided.

S no. Reading along any direction(d1) Reading along perpendicular direction(d2) Observed

diameter

d’= 𝑑1+𝑑2

2

Linear

scale

reading

X

mm

No. of

circular

scale

division

coinciding

(n)

Circular

scale

reading

Y= n×

L.C.

mm

Diameter

D1= x +

y

Linear

scale

reading

X

Mm

No. of

circular

scale

division

coinciding

n

Circular

scale

reading

Y=x +

y

mm

Diameter

d2=x + y

SOURCS OF ERROR:

1. The screw gauge may have backlash error.

2. The threads of the screw may not be of equal pitch.

3. The screw may have friction.

4. The division on linear scale and circular scale may not be evenly spaced.

Government Polytechnic Muzaffarpur

Name of the Lab: Basic Physics lab

Subject Code: 1601107

EXPERIMENT NO. 3

Aim: To determine young’s modulus elasticity of the material of a

given wire.

APPARATUS: Searle’s apparatus, two long identical steel wires of same length

and same area of cross-section, Screw gauge, Meter rod, Slotted weights and

Hanger.

THEORY: Young’s modulus of the given wire is given by

Y= Stress/Longitudinal strain (1)

If L is the original length of the wire having area of the cross–section a and l is the

increase in length produced by a stretching force F acting its length then

Stress= f/a and longitudinal strain= l /L

Y=FL/la. Since F=Mg and a=𝜋𝑟2

Y= MgL /𝜋𝑟2l (2)

Where, r is the radius of the wire.

DISCRIPCTION:

Searle’s apparatus is used to find young’s modulus of a material of a

wire .It is consist of two metal frame M and M’ having two torsion

heads N and N’ at the upper side and two hooks A and B at the lower

side. These frame are held together by a cross piece P and are suspended

from the torsion heads T 1 and T2 by means of two identical wires X

and Y of same material, same length and area of cross-section . A

constant weight W is suspended through a hooks A which keeps the wire

X taut (fig3). A hanger H is suspended from the hooks B. The

experimental wire Y can be loaded by the slipping slotted weights of

magnitude half kilogram each on the hanger H. One end of the spirit

level S is pivoted to the frame M’ and the other end rest on the tip of a

micrometer screw which can be worked in the frame M along a vertical

scale marked in millimeter. The micrometer screw has a circular disc

having equal division along its circumference. The micrometer screw is

adjusted so that the sprit level is in the horizontal position. This is so

when the bubble of the spirit level stands exactly in the center. On

loading the hanger H, the wire Y is elongated and the frame M is

lowered. The micrometer screw is raised till the bubble again stands in

the center. The vertical distance by which the screw is moved measures

the increase in length produced in the wire Y due to the load added on

the hanger.

PROCEDURE:

1. Remove the kinks in the two wires, if any, pulling the wires lengthwise

between two wooden pieces. Now load and unload kilogram weight W on the

hook A to keep the reference wire taut.

2. Find the pitch and least count of the screw gauge. Also determine the zero

correction for the screw gauge. With the help of the screw gauge measure the

diameter of the wire Y at the six different position in two mutually

perpendicular directions at every position.

3. Measure the length of the wire Y with the help of meter scale from the point

of suspension T to the point of attachment N.

4. Find the breaking stress for the steel wire used from the table of constant and

calculate the maximum load to be applied. Maximum load should not exceed

one third of breaking stress.

5. Breaking load=Breaking stress × Area of cross-section.

6. Add a weight of half kilogram on the hanger and weight for a few minute and

adjust the micrometer screw gradually till the bubble of the sprit level exactly

at the center.

7. Go on increasing the load on the hanger H in step of 0.5 kg and observed

the reading on the micrometer each time, after the bubble has been brought in

the center till a load of 3.5 kg is reached. During this observation the

micrometer screw should move in upward direction only so that backslash

error can be avoided.

8. Now unload the wire by removing the weights in the same order (in the step

of 0.5 kg) and take the micrometer reading each time, till all the weights on

the hanger H are removed. During this observation the micrometer screw

should move in downward direction only so that the back slash error can be

avoided.

9. Find the mean reading for each load and calculate the extension for 2.0 kg by

subtracting the first reading from fifth, second from sixth and so on. Find the

mean extension for 2.0kgf. Record all the observation in the table.

Observation:

(a) Measurement of the diameter of the wire

Pitch of the screw gauge = ……..cm

Number of division on circular scale = N = …..cm

Least count of the screw gauge = 𝑃𝑖𝑡𝑐ℎ

𝑁 =……cm

Zero correction = …….cm

Table for calculation of the diameter of the wire

S. No. Reading along horizontal direction Reading along the

perpendicular direction

Mean

observ

ed

diamet

er

Mean corrected diameter = d = d° + zero correction

= ……..cm.

Mean radius = r = 𝑑

2 = …….cm = …….m

(b) Measurement for extension l of the wire

Length of the wire = l = …….cm = …….m

Pitch of the micrometer screw = ……cm

No. of division on a circular scale = N = …..

Least count of micrometer screw = pitch/ N = …..cm

Breaking stress for the wire = …….N/m2

(1/3) rd. of the braking stress = …..N/m2

Table for calculation of extension and load

Table for calculation of extension and load

S. No. Load on hanger H

(kg)

Micrometer reading (cm) Extension for 2

kg wt. l in cm

1

2

3

4

5

6

7

8

Loading

(a)

Unloading

(b)

Mean reading =

a+b/2

Mean extension for 2 kg load = l = …..cm

= …….m

Calculations: Y= MgL/𝜋𝑟2l N/m2

Put all the value of L, r and l in SI units.

Result: The Young modulus of the material (steel) of the wire by Searle’s

apparatus is …. N/m2.

Precaution:

1. There should be no kinks in the wire

2. Do not load the wire beyond the maximum permissible load.

3. The load should be changed in equal steps of 0.5 kg and it should be done

very gently.

Sources of error:

1. The diameter of the wire may change on loading or unloading.

2. The experimental wire may not have a uniform Area of cross- section

throughout its length.

3. Slotted weights used may have standard weight.

1.

Government Polytechnic Muzaffarpur

Name of the Lab: Basic Physics lab

Subject Code: 1601107

EXPERIMENT NO.4

Practical Name: Coefficient of viscosity

Aim: To determine the coefficient of viscosity of given viscus liquid by

measuring the terminal velocity of a given spherical body.

Apparatus:

1. A long glass cylinder of length one meter and diameter 5 cm.

2. Rubber cork.

3. A small glass tube of 0.5 to 1.0 cm internal diameter.

4. Lead shots of different sizes.

5. Stop watch.

6. Meter road.

7. Thermometer.

8. Glycerin.

9. Screw gauge.

10. Plumb line.

11. Cotton thread or gummed paper.

12. Clamp stand.

Theory:

Terminal velocity of a freely falling steel ball-bearing in a homogenous viscus

liquid can be given as.

V = 2𝑟2 (𝜌−𝜎)

9𝜂 (1)

Where v is the terminal velocity of the steel ball- bearing.

r is the radius of the lead shot or steel ball- bearing.

ρ is the density of the lead shot or steel ball- bearing.

σ is the density of the liquid.

η is the coefficient of the viscosity of the liquid.

g is the acceleration due to gravity.

Procedure:

1. Clean the long glass cylinder and fix it with its open end upward with the

help of a clamp stand. Fit the rubber cork in the mouth of the cylinder after

filling it with glycerin and pass the small glass tube through it.

2. Tie two cotton thread loops or paste two pieces of gummed paper at two

point A and B, separated by 50 cm and note the distance between them.

3. Take a steel ball –bearing or lead shot of such a size so that it can pass

easily through the glass tube. Measure its diameter with the help of the

screw gauge in two mutually perpendicular direction and take the mean

diameter.

4. Take a ball-bearing and dip it in a small quantity of glycerin in a watch

glass so that the surface of the lead shot is thoroughly coated with

glycerin.

5. Now take the lead shot or ball-bearing from the watch glass and gently

drop it in the small glass tube so that it falls centrally through the

glasscylinder as shown in figure (4). After moving a few centimeters

through the glycerin, the ball- bearing will attain a uniform terminal

velocity. When the ball-bearing passes down the upper edge of the first

gummed paper A, start the stop watch and stop it when it reaches the

upper edge of the next gummed paper B.

6. Note the time record by the stop watch, and find the terminal velocity of

the ball-bearing by dividing the distance between two gummed papers by

the time recorded by the stop watch.

7. Repeat the steps 3, 4, 5 and 6 by dropping four ball – bearing of same size.

8. Repeat the steps 3, 4, 5 and 6 by dropping four more ball bearing of

different sizes.

9. Note the temperature of the glycerin at the beginning and at the end of the

experiment and take its mean value. Also note the density of the glycerin

and material of the ball-bearing from the table of constants.

10. Record all the observation in the table.

Observation:

Least count of the stop watch = …….. s.

Least count of the screw gauge = …….. cm.

Zero correction for screw gauge = …….... cm.

Mean temperature of the glycerin = ……… c0.

Density of glycerin = ………gcm-3

Density of small ball-bearing = ……….gcm-3

Distance between two gummed paper marks = …….. cm

Table for calculation of terminal velocity and radius of ball-bearing

S.

No.

Time taken to fall

distance S

Terminal

velocity v

= 𝑺

𝒕

Cm/s

Diameter of the ball-bearing

(cm)

Mean

corrected

diameter d

= d0+ zero

error

cm

Radius

r= d/2

cm

a

s

b

s

Mean

time

t =

(𝒂 + 𝒃

𝟐)

s

Along

PQ

cm

Along

RS

cm

Mean

obs.

Diameter

d0 = 𝑷𝑸 + 𝑹𝑺

𝟐

cm

1.

2.

3.

4.

Calculation:

Plot a graph between radius r2 and terminal velocity v taking r2 along X- axis and

v along Y- axis. The graph between r2 and v is straight line as shown in figure.

Find the slope of straight line by taking two point A and B on the line.

Slope of the straight line = 𝐵𝐶

𝐴𝐶 =

𝑣

𝑟2

= 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝑣 𝑎𝑡 𝐺−𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑣 𝑎𝑡 𝐹

𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝑣 𝑎𝑡 𝐸−𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑣𝑎𝑡 𝐷

This slope will give the value of v/ r2,

r2/v =𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝑟2 𝑎𝑡 𝐸−𝑣𝑎𝑙𝑢𝑒 𝑜𝑓𝑟2 𝑎𝑡 𝐷

𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝑣 𝑎𝑡 𝐺−𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑣 𝑎𝑡 𝐹

η = 2

9 (ρ-σ) g.

𝑟2

𝑣

On putting the value of r2/v in equation (2) and also put the value of ρ, σ and g we

can calculate the value of coefficient of viscosity using equation (2).

Term

inal

vel

oci

ty v

(cm

/s)

F

G

G

G

G

B

C

E D

A

Radius (r2) in cm2

Result:

The graph between terminal velocity (v) and (radius)2 comes to be straight line.

The value of coefficient of viscosity for glycerin at temperature T0C is …poise.

Precaution:

1. The steel ball-bearing should be of small size so that they take longer time to

fall through the given distance.

2. The ball-bearing should be dropped gently.

3. The ball-bearing should fall along the central axis of glass cylinder.

4. The ball –bearing should be thoroughly coated with the given viscous liquid.

5. Diameter of the ball-bearing should be measured in two mutually

perpendicular direction.

6. The liquid should be highly viscous

Sources of error:

1. The ball-bearing may not be perfectly spherical.

2. The liquid may not have uniform density.

3. The observed velocity may not be constant.

Government Polytechnic Muzaffarpur

Name of the Lab: Applied science lab

Subject Code: 1602107

EXPERIMENT NO- 5 Practical Name: tension of water by capillary rise method

Aim: To determine the surface tension of water by capillary

rise method.

Apparatus:

1. Three glass capillary tube of different bores.

2. Travelling microscope.

3. Adjustable stand.

4. A flat bottom glass dish.

5. Clamp stand.

6. A glass strip

7. A needle.

8. Thin rubber bands.

9. A thermometer.

10. Clean tap water whose surface tension is to be

determined.

Theory: The surface tension of the liquid is given by

T = (1)

For water the value of angle of contact θ is very small.

Hence cosθ = 1 (θ = o; cosθ = 1)

The surface tension of the water can be given as

T = (2)

Where,

T= is the surface tension of the water.

r is the radius of the capillary tube.

h is the rise of water in capillary tube above the free

surface of the water.

D is the density of the water at room temperature.

g is the acceleration due to gravity.

Procedure:

(a) Seating the capillary rise tube apparatus

(1) Clean the capillary tube and flat bottom glass dish with

alkaline solution (caustic soda) and the with water and

dry them.

(2) Fill the glass dish with water (free from dirt and gases)

and place it on the adjustable stand whose height can be

adjusted. Make it base horizontal by levelling screw.

(3) Mount the capillary tube C whose diameter are ranging

from 0.1 mm to 0.5 mm on a glass plate with the help of

rubber bands. Set the glass plate vertically over the dish

containing water by holding it in a clamp stand and

adjust the position of adjustable stand so that ends of

capillary tubes are well within water as shown in figure.

(4) Mount a fine needle on the glass plate which is parallel

to the capillary tube with its tips just touches the water

surface as shown in figure.

(b) Measurement of capillary rise

(5) Find the least count of travelling micro scope for

horizontal and vertical scale and record them.

(6) Rise the microscope to a suitable height , keeping its

axis horizontal and view the water meniscus in the first

capillary tube ( which has maximum rise)

(7) Make the horizontal cross wire just touches the central

part of the concave meniscus. ( it looks convex through

the microscope as shown in figure) Take the reading on

the vertical scale of the microscope.

(8) Now move the microscope horizontal and bring it in

front of second capillary tube.

(9) Lower the microscope and repeat the step n7 for the

second capillary tube.

(10) Now repeat the step 8 and 9 for third capillary tube.

(11) Now move the microscope horizontal and bring it in

front of the needle.

(12) Now lower the microscope till the horizontal cross-wire

is midway between the pointed end of the needle and its

image in water as shown in figure. Note this reading of

the microscope on the vertical scale. This gives the

position of the free surface of the water.

(13) Note the temperature of the water with the help of the

thermometer.

(c) Measurement of internal diameter of capillary tube

(14) Plate the capillary tube horizontally on the adjustable

stand.

(15) Focus the microscope on fine hole of the tube and

measure its internal diameter in two mutually

perpendicular directions PQ and RS as shown in figure.

Repeat this procedure to find the internal diameter of

the other two tubes.

(16) Record all the observation in the tables given below.

Observation:

Least count of the travelling microscope = …. = cm

Table for calculation of height of the water risen in capillary tubes

Table for calculation of height of the water risen in capillary tubes

S. No.

of

Capillary

Tube

cm

Reading of water meniscus Reading of the tip of h =

h1 – h2

cm Main

Scale

Reading

A

cm

No. of

V.S.

division

coinciding

‘n’

cm

Total

Reading

h1 = A+

n × L.c.

cm

Main

Scale

Reading

Aʹ

cm

No. of

V.S.

division

coinciding

‘n’

cm

Total

Reading

h2 = A+

nʹ × L.c.

cm

S. No.

of

Capillary

tube

Microscope reading at

Horizontal

Diameter

D1 = PQ

(cm)

Vertical

diameter

D2 = RS

(cm)

Mean

diameter

D = d1+d2 /2

( cm)

Mean radius

R= d/2

(cm)

P

Q

R

S

Temperature of the water = t0 = ….0C

Density of the water at t0 = d = ……gcm-3

Calculations:

We have the relation

T = ===================================================================================

T = ……dynes/cm = ……..× 10-3Nm-1

Now substitute the value of h and r for each capillary tube

and calculate the value of T

Mean value of T = (T1+T2+T3/3) = ….dynes/cm

= ….. Nm-1

Precaution:

(a) Capillary tube should be clean and liquid should

be free from dirt and grease.

(b) Capillary tube and needle should be set vertical.

(c) Microscope screw should be moved in lower

direction only to avoid backlash error.

(d) Do not use distilled water.

(e) Internal diameter of capillary tubes should be

measured along two mutually perpendicular

directions.

(f) Capillary tubes should be of uniform bores.

(g) Temperatures of the water should be measured in

the beginning and also at the end as surface

tension is very sensitive to the temperature.

Sources of error:

(a) Contamination of water surface can not be ruled

out.

(b) Capillary tubes may not have uniform bore.

Government Polytechnic Muzaffarpur

Name of the Lab: Basic Physics lab

Subject Code: 1601107

EXPERIMENT NO- 6

Practical Name: Verification of Boyle’s law

Experiment-6

Aim:- To Verify Boyle’s Law

Materials used: A Boyle’s Law Apparatus, Air Pump, Hand Vacuum

Pump.

Method:

1) Set up apparatus as shown in the diagram.

2) Connect air pump to the in let of the oil reservoir.

3) Open air tap and pump in air until pressure

gauge reads its max value.

4) Quickly close tap.

5) Leave for a minute or two, after changing the

pressure of the trapped air wait a minute or two

before reading the pressure or volume, to allow

the air to reach room temperature. This is

necessary because when the air is compressed

or expanded there may be slight changes in

temperature.

6) Then measure the gas pressure by reading it off

the Bourdon gauge. Record these volumes.

7) Read the volume of gas off the scale next to the glass tube.

8) Gently open then quickly close tap to release some air.

9) Leave for a minute or two, then measure the gas pressure by reading it off

the Bourdon gauge.

10) Record these values.

11) Repeat steps 7-9 at least six times until the pressure of the gas is

back to atmospheric pressure

12) Plot a graph of pressure (p) against the inverse of volume (1/V)

Results:

The graph is a straight line through the origin, verifying that the pressure (p) is

proportional to (1/V), verifying Boyles Law. Also all values of pV are the same.

P α 1/V therefore p=k(1/V) therefore pV=k

Results:

Pressure

p/ atms

Volume

V/cm3

1

Volume /cm-3

120 9.0 0.11

180 6.0 0.17

220 5.0 0.20

280 4.0 0.25

320 3.5 0.29

380 3.0 0.33

440 2.5 0.40

pV=k

To graph p against 1/V

Boyles Law States……. That at constant temperature the volume of a fixed

mass of gas is inversely proportional to its pressure.

P α 1/V

This proves Boyles law as it is a straight line graph through the origin. That graph is P

α 1/V

0

50

100

150

200

250

300

350

400

450

500

0 0.1 0.2 0.3 0.4 0.5

Precautions:

1) After changing the pressure of the trapped air wait a minute or two before

reading the pressure or volume, to allow the air to reach room temperature.

This is necessary because when the air is compressed or expanded there may

be slight changes in temperature which will affect t the volume of gas )due

to expansion or contraction)

2) When reading volume make sure your eye is level with the Mercury

Meniscus.

3) Make sure air is connected tightly to oil reservoir in let.

4) If a hand suction pump is available you will be able to reduce the pressure of

the gas below atmospheric pressure. You can then take a future series of

values of p and V include them in the table and graph.

Government Polytechnic Muzaffarpur

Name of the Lab: Basic Physics lab

Subject Code: 1601107

EXPERIMENT NO- 7

Practical Name: Measurement of temperature using

Thermocouple.

Experiment-7

Setup:

The setup consists of a shielded K-type thermocouple, its signal

conditioning unit, an immersion heater and a beaker. The thermocouple

has two terminals which are connected to the signal conditioning unit. In

the signal conditioning unit has a milli volt source that provides -10 to

+25 mV to calibrate the signal conditioner module for measurement of

temperature directly in oC. There is a zero and gain adjustment POT

provided for the calibration purpose. A 4 digit seven segment display is

there for displaying the output (mV or in degree Celsius) in digital form.

Working:

The thermocouple is immersed in a hot water whose temperature is to

be measured. The output of thermocouple is in mV which is directly

proportional to the temperature that the thermocouple sense. The output

of the thermocouple is connected to the signal conditioning unit where it

is directly fed to a DC differential amplifier and then is fed to a summing

amplifier. The summing amplifier has a gain and zero adjustment POT to

obtain output directly in engineering unit of temperature. An LM35 IC

temperature sensor is used for sensing ambient temperature that takes

care of the ambient temperature compensation.

Apparatus required:

Beaker with water.

An immersion heater

A thermometer

A multimeter

Procedure:

To get thermocouple output in mV:

Fill the water in beaker. Place an immersion heater in the beaker and

keep the thermometer as well as the thermocouple in the beaker too.

Connect the output of the signal conditioner with the DPM by a patch

cord (between T2 and T3). Switch ON the power. Put the toggle switch

towards mV side. Set gain adjustment pot at anticlockwise i.e set

minimum gain. Short the input (Thermocouple) of the setup with a patch

cord and measure the output on DPM (Digital Panel Meter). It must be

zero, if not adjust it to zero with the help of zero pot. Remove the input

short lead and connect the I/P with a millivolt source having reading

10mV (measure with a multimeter). The reading on DPM is in mV and

set it to 10.00 with gain adjustment POT. Remove the millivolt source

from the input and connect the thermocouple terminals. Switch ON the

heater to heat the water. The millivolt generated across the

thermocouple terminals will be displayed on the DPM. Note down the

reading of both thermocouple and thermometer after a fixed time

interval. Plot the graph between temperature indicated by thermometer

and thermocouple emf(mV).

Observation:

Sl no. Time interval Temperature by thermometer DPM reading

(mV)

To get thermocouple output directly in degree Celsius:

Disconnect the thermocouple from the input and short again by a patch

cord. Toggle the switch towards oC. note down the reading on DPM

which is ambient temperature. Remove the short lead and connect the

millivolt source and set the value at 4.1mV by multimeter. Adjust the

DPM reading at 100+ambient temperature with gain adjustment pot.

Remove the millivolt source and connect the thermocouple and note

down the reading at different temperature position by heating the water.

Observation:

Sl

no

Time interval Temperature by

thermocouple

Temperature by

thermometer

Government Polytechnic Muzaffarpur

Name of the Lab: Basic Physics lab

Subject Code: 1601107

EXPERIMENT NO- 8

Practical Name: :- Determination Of Coefficient Of

Linear Expansion Of A Solid By Pullinger’s Apparatus.

Aim:- Determination Of Coefficient Of Linear Expansion Of A Solid By

Pullinger’s Apparatus.

Pullinger's Apparatus

Construction

The linear expansivity of a material can be determined by the Pullinger’s

apparatus. It consists of a hollow cylinder where the experimental rod is

placed inside the cylinder. There are three opening in the cylinder. The

upper and lower opening are used for steam inlet and steam outlet. The

middle opening is used for placing thermometer which measures the

temperature of rod. The spherometer is placed in a free end of the

instrument which measure the increase in length of the rod. An electric

circuit is connected with the instrument to find whether spherometer

touches the rod or not.

Working

The experimental rod is taken and its length is measured (say) L. The rod

is placed inside the cylinder and the initial temperature of the rod is taken

(say)θ1. Now the spherometer is rotated downward when it just touches the

rod. Initial reading on spherometer is taken and spherometer is rotated

upward to give a small space for expansion of the rod. The steam is

passed into the cylinder as steam is passed the reading in thermometer

rise. When the thermometer shows constant reading 8-10 the final

temperature of the rod is taken (say)θ2.The spherometer is rotated

downward when it touches the rod and the final reading of spherometer is

taken. let initial spherometer reading is R1and final reading is R2. Thenthe

increase in radius is R2 - R1.

We have

Linearexpansivity=increaseinlengthoriginallength×riseintemperatureL

inearexpansivity=increaseinlengthoriginallength×riseintemperature

∴α=R2−R1R1(θ2−θ1)∴α=R2−R1R1(θ2−θ1)

By finding values of R1, R2,θ2,θ1θ2,θ1and linear expansivity is determined.

Forces setup due to expansion

Force Set up Due to Expansion or Contraction

Let us consider a metal rod of length l1 is fixed at the two rigid fixed ends

S1 and S2 as shown in the figure. Suppose the initial temperature be θ1.Now

the rod is heated up to θ2,metal rod will try expand to the length of l2, but it

cannot do so.

From linear expansion of solid, we have

l2=l1(1+αΔθ)l2=l1(1+αΔθ)

Where αα is the coefficient of linear expansion of the rod,

and Δθ=θ1−θ2Δθ=θ1−θ2 .So, the increase in length is

l2−l1=l1(αΔθ)l2−l1=l1(αΔθ)

Due to increase in temperature, the rod tries to expand but will not be able

to, to expand due to rigid ends. As a result, a force or tension is produced

which would compress the rod. From the definition of Young’s modulus of

elasticity, we have,

Young’s modulus, Υ=tensile stresstensile strain=tension/area change in length/original

length=T/Al2−l1/l1Υ=tensile stresstensile strain=tension/area change in

length/original length=T/Al2−l1/l1

Where A is a cross-sectional area of the rod. Then,

Υ=TA×l1l2−l1=TA×l1l1αΔθ=TAαΔθΥ=TA×l1l2−l1=TA×l1l1αΔθ=TAαΔθ

Or, T=ΥAαΔθT=ΥAαΔθ

Tension or force =ΥAα(θ1−θ2)=ΥAα(θ1−θ2)

Bimetallic Thermostat

Bimetallic strip (a) At normal temperature, (b) At higher temperature

Bimetallic thermostats are used to control higher temperature. It works as

an electric contact breaker in an electrical heating circuit. It consists of two

strips of metal that have different coefficients of linear expansion such as

brass and steel. The two pieces are welded and riveted together. When the

bimetallic strip is heated, the brass, having a greater value of, expands

more than the steel. Since the two strips are bounded together, the

bimetallic strip bends into the arc as shown in the figure. The metallic strip

is in contact with screw S at point P and on heating, the strip curves

downwards and the contact at P is broken. Thermostats are used for

controlling the temperature of laundry irons, hot water storage tanks,

aquaria for tropical fish and for many other purposes.

Differential expansion

When metal rod of different metal are heated to the same range of

temperature their expansion are different i.e. differential expansion.

Let us consider two rod B and C having length and with linear expansivity

and respectively. Both the rods are heated so that the final length of the rod

are and respectively at the temperature.

We have,

l2=l1(1+αΔθ)l2=l1(1+αΔθ)

Δθ=θ2−θ1Δθ=θ2−θ1

Increase in length of rod ββ

For equal difference in length

l2−l1=l1αΔθl2−l1=l1αΔθ

or, l1αΔθ=l′1α′Δθl1αΔθ=l1′α′Δθ

or, l1α=l′1α′l1α=l1′α′

or, l1l′2=α′αl1l2′=α′α

This is the constant difference in length in all temperature.

Illustration for real and apparent expansion of liquids.

Relation between real and cubical expansion of liquid

Liquid does not have fixed shape so, we do not take linear and superficial

expansion in the case of liquid instead we take cubical expansion.

Let us consider liquid contain in a vessel having an original volume up to

level A suppose the system is heated at first. After heating the expansion of

vessel takes place and the level of a liquid decreases to point B. After

sometimes liquid gets heated the expansion of a liquid is greater than that

of solid. So, finally liquid reaches C.

Here,

AB = expansion of vessel

AC = apparent expansion of liquid

BC = real expansion of liquid

From the figure

BC = AC + AB ----------(i)

BC=AC+AB…(i)BC=AC+AB…(i)

real expansion of liquid = apparent expansion of liquid + expansion of a

vessel

Real expansivity of liquid (γr)(γr) is defined as real increase in volume of

the liquid per unit original volume of the liquid per unit rise in temperature.

.i.e

Real expansivity of liquid (γr)=Increase in volume of the liquidoriginal volume of the

liquid× rise in temperatures(γr)=Increase in volume of the liquidoriginal volume of

the liquid× rise in temperatures

γr=BCV×Δθγr=BCV×Δθ

∵original volume of liquid=volume of vessel(V)×rise in

temperatureΔθ∵original volume of liquid=volume of vessel(V)×rise in

temperatureΔθ

BC=γrV×Δθ…(ii)BC=γrV×Δθ…(ii)

Apparent expansivity is defined as an apparent increase in a volume of

liquid per unit rise in temperature.

apparent expansivity of liquid (γa)=apparent increase in volume of the liquidoriginal

volume of the liquid× rise in temperature(γa)=apparent increase in volume of the

liquidoriginal volume of the liquid× rise in temperature

γa=ACV×Δθ γa=ACV×Δθ

AC=γaV×Δθ…(iii)AC=γaV×Δθ…(iii)

Cubical expansivity is defined as increase in a volume of the vessel per unit

original volume of the vessel per unit rise in temperature.

Expansion of vessel (γ)=increase in volume of the vesseloriginal volume of the

vessel×rise in temperature(γ)=increase in volume of the vesseloriginal volume of

the vessel×rise in temperature

γ=ABV×Δθγ=ABV×Δθ

AB=γV×Δθ…(iv)AB=γV×Δθ…(iv)

Using equation (i), (ii), (iii) and (iv)

γrV×Δθ=γaV×Δθ+γV×ΔθγrV×Δθ=γaV×Δθ+γV×Δθ

γrV×Δθ=(γa+γ)V×ΔθγrV×Δθ=(γa+γ)V×Δθ

γr=γa+γγr=γa+γ

γr=γa+3α[∵γ=3α]