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Simple Pendulum Experiment (Class 11) Readings

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Simple Pendulum Experiment (Class 11) with Calculations and Readings

Aim


i. To verify the relation between period (T) and length (l) of pendulum

ii. To find out the acceleration due to gravity

iii. To determine the length of seconds pendulum

iv. To find the period of the pendulum whose length is 105 cm.


Apparatus


Simple pendulum, Stop-watch, Meter scale, Wooden block etc..


Principle


For small amplitudes of oscillation of a simple pendulum,

l/T2 = a constant where, l —> Length of the pendulum

T—> Period of the pendulum

Also, T = 2π(l/g) where, g —> Acceleration due to gravity at the place

Therefore, g = 4π2(1/T2)


Procedure


i. Relation between I and T2


The bob is placed between two wooden blocks and its diameter (d) is measured. Hence radius (r = d/2) can be calculated. The length of the string (I) is so adjusted that the distance between the point of suspension and the bottom of the bob is (50 + r) cm. Hence the length of the pendulum ‘l’ is 50 cm.


A mark is made on the edge of the table using a piece of chalk to indicate the equilibrium position of the pendulum, ie. , the position of the pendulum when it is at rest. The bob is pulled aside through a small distance and released. The pendulum executes oscillations, after a few oscillations, a stop watch is started just when the pendulum crosses the equilibrium position. When it next crosses the mark in the same direction, the oscillations are counted and when the pendulum passes the chalk mark in the same direction for the 20th time, the stop watch is stopped.


Thus the time taken for 20 oscillations is determined. This is repeated and the mean time taken for 20 oscillations is found. Hence the time for one oscillation ie., period 'T' is calculated. l/T2 is also calculated.


The experiment is repeated for lengths 60, 70, 80, 90, 100,110 cm. In each case l/T2 is calculated. It is found to be a constant. This is the relation between the period and length of a simple pendulum. Graph is drawn with 'l' along the X-axis and 'T2' along the Y-axis. A straight line graph is obtained.


ii. Acceleration due to gravity at the place


The mean value of l/T2 is determined. Hence 'g' can be calculated using the formula g = 4π2(1/T2). Note AB and BC from the graph. Hence g can be calculated using the equation, g = 4π2.AB/BC


iii. Length of the seconds pendulum


For a seconds pendulum, T = 2 seconds. Then T2= 4. From the graph, the value of 'l’ for which T2 = 4 is found (OD). This gives the length of the seconds pendulum.  


iv. Period of the pendulum whose length is 105 cm


From the graph the square of the period corresponding to the length 105 cm is noted (OE). The square root of this ( OE ) gives the period.


Observations and Readings


Radius of the bob, r = 0.95 cm


No:

Distance between point of suspension and the bottom of the bob (l+r)

Length of the pendulum (l)

Time for 20 oscillations (t)

Period of oscillation (T=t/20)

T2

l/T2

1

2

mean

 

cm

cm

s

s

s

s

s2

cm/s2

1

2

3

4

5

6

7

50.95

60.95

70.95

80.95

90.95

100.95

110.95

50

60

70

80

90

100

110

28

30

31

34

35

38

40

28

30

31

34

35

38

40

28

30

31

34

35

38

40

1.4

1.5

1.55

1.7

1.75

1.9

2

1.96

2.25

2.40

2.89

3.06

3.61

4

25.5

26.7

29.7

27.7

29.4

27.7

27.5

 

Mean value of 1/T2 = 27.661 cm/s2 = 0.276 m/s2

Therefore, Acceleration due to gravity, g = 4π2(1/T2) = 4 x (3.14)2 x 0.276 = 10.896 m/s2


l – T2 graph

From graph:


AB = 43 cm = 0.43 m

BC = 1.5 s2

G = 4π2(AB/BC) = 4 x (3.14)2 x 0.43/1.5 = 11.30 m/s2


Length of the seconds pendulum (OD) = 110 cm = 1.10 m

Period of the pendulum whose length is 105 cm = OE = 1.92 s

 

Results

 

i. l/T2 is found to be a constant

ii. Acceleration due to gravity at the place,

(a) by calculation = 10.896 m/s2

(b) from graph = 11.30 m/s2

iii. Length of the seconds pendulum =1.10 m

iv. Period of the pendulum whose length is 105 cm = 1.92 s

Investigatory Project on Air Pollution

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Investigatory Project on Study of Pollutants in Air (Class 12)

Introduction


Atmosphere acts as an insulating blanket around the earth. It is the source of essential gases, and it keeps day and night temperatures. It becomes a shield and protects the earth from UV radiations and meteors. Normal composition of clean air in the atmosphere is as follows.


Gases                                   

Volume

Nitrogen

Oxygen

Argon

Carbon Dioxide

Methane

Hydrogen

Other gases

78.08%

20.95%

0.934%

0.0314%

0.0002%

0.00005%

little

 

But, due to pollution, the concentrations of the different gases show variations. Besides, a number of harmful gases are also added into the atmosphere. These affect air quality adversely and make it unfit for the survival of organisms. Air pollution results from gaseous emissions from industries, thermal power stations, automobiles, domestic combustion, etc. Undesirable substances are added into the atmosphere through human activities also. Besides, volcanic eruptions, forest fires and natural decays give out large quantities of harmful dust and sulphur compounds into the air.


Pollutants are the substances which cause adverse effect on the natural quality of any component of the environment. Air pollutants can be conveniently classified into two main groups. They are Gaseous pollutants and Particulate matter.


Gaseous pollutants: They are pollutants which are usually gaseous in nature under normal temperature and pressure. They may be primary or secondary in nature. Primary pollutants enter the atmosphere directly from various sources (carbon monoxide, hydrocarbon, sulphur dioxide etc.). Secondary pollutants are formed during chemical reactions between primary air pollutant and other atmospheric constituents like water vapour, light (eg: photochemical smog and PAN – Peroxy Acetyl Nitrate). Gaseous pollutants includes oxides of carbon, oxides of sulphur, hydrogen sulphide, hydrocarbons, oxides of nitrogen, ozone and other oxidants.


Particulate pollutants: Particulate matter includes solid particles or liquid droplets which remain suspended in the air. Smoke, photochemical smog, dust, soot, asbestos fibres, radioactive elements, aerosols, etc. are the particulate air pollutants. The sources of particulate pollutants are fuel combustion and industrial operations, handling, loading and transfer of industrial materials agricultural operations and construction works and automobile exhaust. Besides, many kinds of biological particulate matter also remain suspended in air. They include pollen grains, spores, bacterial cells, fungal spores etc.


Aim:


To examine the process of particulate matter in the air


Materials and methods


A leaf of a plant growing in the open area, a leaf from a plant growing in a glass house, slides, cover slips, white handkerchief/cotton wool, brush, microscope etc.


Procedure 1


Pluck a leaf from a plant growing in the open area. Pour a few drops of glycerine over it and rub it with a clean brush. Take a drop of glycerine from the leaf over a clean slide and cover it with the cover slip. Observe it under the microscope. Repeat the experiment by taking a leaf from the plant growing in a glass house.


Observation: The slide prepared from the leaf of a plant growing in the open area shows the presence of number of pollutants such as dust, pollen grains and spores etc.


Procedure 2


See a beam of light entering inside a dark room through a window.


Observation: A number of dust particles and other particulate pollutants are seen moving here and there in the beam of light.


Procedure 3


When you come back from the school or from any other busy places, wipe your face with a clean handkerchief or cotton wool.


Observation: A large amount of pollutants get collected on the hand kerchief or cotton wool.


Procedure 4


Apply some glycerine on a clean slide. Keep the slide outside for the whole day. Now examine the slide under the microscope.


Observation: A number of types of pollen grains, spores of number of fungi, dust particles, soot etc. are seen sticking on the slide.


Conclusion


The air contains a number of particulate pollutants. The concentration of pollutants is variable in different localities.

Investigatory Project on Water Pollution

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Investigatory Project on Water Pollution

Introduction


The addition of any substance (pollutants) which degrades the quality of water so that it either becomes health hazard or unfit for use is called water pollution. Most of the water surfaces usually contain small quantities of suspended particles, organic substances and a number of living organisms (bacteria, algae, fungi, protests, viruses etc.). Increase in the concentration of these substances pollutes water and makes it unfit for use. Similarly the presence of a low concentration of poisonous or toxic chemicals also pollutes water. The nutrient enrichment and algal growth result in the depletion of oxygen in water. It is called eutrophication. Water pollution due to organic waste is measured in terms of biological oxygen demand (BOD). It is the amount of dissolved oxygen needed by bacteria to decompose the organic wastes present in water.

 

Experiment 1

 

Aim

 

To test the presence of particulate matter in a given sample of water.

 

Materials Required

 

Cardboard box, electric bulb, beaker, sample of water.

 

Procedure

 

Take a cardboard box and prepare a Tyndal set up from it to test turbidity. Tyndal set-up can be prepared by making a cardboard box and make a pencil size hole in the box on opposite sides. Then fix a light source on one hole of the box. Inside the box at the centre, keep a beaker containing the sample of water. Switch on the light source and observe the sample of water through the hole. (Obtain the sample of water from different sources and compare their turbidity)

 

Observation

 

Suspended particulate pollutants may be observed.

 

Experiment 2

 

Aim

 

To study the biochemical oxygen demand of the given sample of water.

 

Materials and methods

 

Beaker, pipettes, burettes, conical flask, stirrer, ferrous sulphate solution, pheno saffranin (phenolphthaline + saffranin), Fehling solution, water sample.

 

Procedure

 

1. Take the burette, fill it with ferrous sulphate solution and fix it on a stand.


2. Take 50 ml of water sample to be tested in a beaker and add 2-3 drops of pheno saffranin and 10 ml of Fehling solution to the water sample.


3. Set the burette in such a way that its lower end remains in the water of the beaker.


4. Now run the ferrous sulphate solution and keep stirring the water sample till the pink colour disappears and the colour of water becomes light bluish green.


5. Note the initial and final readings of the burette and calculate the amount of ferrous sulphate used.


6. Repeat the experiment with different samples of water and record the volume of ferrous sulphate used to decolourise the pink colour.

 

Observations


Sl No:

Water Sample

Ferrous sulphate reading in burette

Volume Fe2SO4 used (X – Y)

Inference

Initial reading (X)

Final reading (Y)

1

2

3

4

5

 

 

 

 

 

 

 Conclusion

 

The oxygen dissolved in water oxidises ferrous sulphate to ferric sulphate. As a result, pink colour of the indicator disappears. The sample of water which requires higher volume of ferrous sulphate to decolourise the pink colour contains lesser dissolved oxygen and this has higher BOD. This shows greater pollution due to the presence of large number of microorganisms.

Transistor Characteristics Experiment with Readings

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COMMON EMITTER TRANSISTOR CHARACTERISTICS EXPERIMENT (CE Configuration Lab Report) (Class 12)


Aim


To study the static characteristic of a CE transistor


Apparatus


npn or pnp transistor (e.g. B.D 139 or B.D 140), a 2V and a WV batteries, rheostats, keys, milliammeter, microammeter, two low range voltmeters etc.


Procedure

Connections are made as shown in figure. The rheostat Rh1 is used to vary input voltage VBE and it is read from voltmeter V1. The input current IB is measured using a microammeter (µA ). The output voltage VCE is varied using Rh2 and readings are noted from voltmeter V2. The output current lC is measured by the milliammeter (mA).


Input characteristic


VCE is kept 1V and VBE is varied from zero in steps of 0.1 V(say) upto the rated voltage. IB is noted in each step. Graph is drawn with VBE along the x-axis and IB(µA) along the y-axis. [The reciprocal of the slope of the input characteristic gives the input resistance ri]


To draw the output characteristics


It is the graph drawn with output current IC - taken along y-axis and the output voltage VCE - taken along x-axis. IB is kept constant by adjusting Rh1, say, at 20 µA . Now VCE is increased in steps of say, 0.5 V upto the maximum rated voltage by adjusting Rh2. IC is noted in each step. A graph is drawn with IC along the y-axis and VCE along the x-axis. This gives the output characteristic corresponding to IB = 20µA. The experiment is repeated keeping IB constant, say 40 µA, 60µA, 80 µA, …. etc. and similar graphs are plotted. [The reciprocal of the slope of the graph gives the output resistance (r0))


The current gain β = (IC/IB)


Observation Table and Readings


Input Characteristics


VBE (V)

VCE = 2V

IB  (µA)

VCE = 4V

IB  (µA)

0

0

0

0.1

0

0

0.3

0

0

0.5

0

0

0.6

12

12

0.7

48

44

0.8

86

76

0.9

148

144

1

200

200

 

Output Characteristics


VCE (V)

IB (80µA)

IC

IB (120µA)

IC

0

0

0

0.2

9

16

0.4

12

17

0.6

14

17

0.8

14

17

1

14

17

2

14

17

3

14

17

4

14

17

  

Results


i. The characteristics of the transistor in CE configuration are drawn.

ii. The input resistance of the transistor = ……. Ω

iii. The output resistance of the transistor = ……… Ω

Concave Lens Experiment (Class 12) Readings

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Concave Lens Experiment (Class 12) Readings


Aim


To determine the focal length of a concave lens using convex lens.


Apparatus


Concave lens, A convex lens of short focal length, Lens stands, illuminated wire gauze , Screen, Metre scale etc.


Principle


i. Lenses in contact


When a convex lens of focal length (f1) and a concave lens of focal length (f2) are placed coaxially in contact with each other, the equivalent focal length (F) of the combination is given by


1/F = 1/f1 +1/f2


Therefore, f2 = Ff1/(f1 - F)


The focal length (f2) of a concave lens is negative,


ii. Lenses out of contact


The focal length of the concave lens when it is out of contact with a convex tern it given by,


f2 = uv/(u- v)


where,

u —> Distance of the concave lens from the virtual object

v —> Distance of the concave lens from the image

 

Procedure

 

i. Lenses in contact

The focal length (f1) of the given convex lens (short focus) is determined by v method. The given concave lens is kept in contact with the convex lens. The focal length of the combination (F) is also determined by u - v method. Then focal length (f2) of the given concave lens can be calculated .

 

ii. Lenses out of contact

The given convex lens is fixed on a stand. It is fixed amid an illuminated wire gauze and a screen. The position of screen is adjusted to obtain a clear picture of the wire gauze on the screen at I. The concave lens (L) is fixed between the screen and the convex lens without any further arrangement. The distance amid the screen and the concave lens, LI1 = u is calculated. Now the screen alone is moved back to obtain a clear image I2 on the screen. The distance LI2 = v is measured. Using the values of u and v the focal length of the concave lens can be calculated. The experiment is repeated by changing the values of LI1 = u.

 

Observation Table and Readings


i. Lens in contact


Focal length (f1) of convex lens by displacement method

Trial

D cm

d cm

f1 = (D2-d2)/4D

Mean Focal length (f)

1

80

10.5

19.66

f1 = 19.74 cm

2

82

15

19.81

 

Lens used

No:

Distance between lens and object (u)

Distance between lens and image (v)

Focal length

Mean Focal length (f)

-

-

cm

cm

cm

cm

Combination of convex and concave lens

1

2

76.5

85.5

77.5

73.5

38.49

39.52

F = 39.005

 

Focal length of the concave lens, f2 = Ff1/(f1-F) = 39.96 cm = 39.96 x 10-2 m

 

i. Lenses out of contact


No:

Distance of first image I1 from concave lens (LI1 = u)

Distance of second image I2 from concave lens (LI2 = v)

Focal length (f2)

 

cm

cm

cm

1

2

3

29

39.5

32.1

15.5

20

16.5

-33.95

-40.51

-33.29

 

Mean focal length, f = -35.91 cm = -35.91 x 10-2 m

 

Results


Focal length of the concave lens


i. by lenses in contact method = -39.96 x 10-2 m

ii. by lenses out of contact = -35.91 x 10-2 m

 

Viva Questions and Answers

 

1.Give the nature, position and size of the image formed by a concave lens at different positions of the object.


Position of

Nature

Size

Erect or inverted

Object

Image

At infinity

At F

Virtual

Diminished

Erect

Any other position

Between F and C

Virtual

Diminished

Erect

 

2. What do you understand by the term 'focal plane' of a lens?


It is a plane perpendicular to the principal axis and at a distance equal to the focal length of the lens.


3. What is spherical aberration in a lens? How is it eliminated?


It is the inability of a lens to focus all the refracted rays to a single point. It can be minimised by using stops.


4. What is chromatic aberration? Flow is it eliminated?


The inability of a lens to focus all the colours to a single point is called aberration.


Chromatic aberration can be eliminated by combining a convex lens and a concave lens of suitable focal length and material (achromat).


5. What is lens maker's formula?


1/f = (n-1)[1/R1-1/R2]


6. Why is the focal length of a concave lens negative?


This is because the focal length is measured in a direction opposite to the incident ray.