Object: To determine the surface tension of water from capillary rise method.

Transcription

1 Object: To determine the surface tension of water from capillary rise method. Apparatus: Travelling microscope, Adjustable stand, Beaker, Capillary Tube, Thermometer. Theory: Let a capillary tube open at both ends be inserted vertically in a liquid of density d and surface tension T, in such a way that only its lower end dips in the liquid. It will be found that a column of liquid rises up in the capillary. It will be found that a column of liquid rises up in the tube through a height h above the free surface of the liquid and the surface tension of the liquid T acts along the tangent to the meniscus. The component of the surface tension acting vertically upwards is T cos a, where a is the angle of contact. If r is the internal radius of the capillary tube, then the total force acting, upwards on the mansions is T cosα X 2πr. This force of surface tension acting upward around the circle of contact supports the weight of the column of liquid below the meniscus. So we have for the equilibrium of the liquid column- 2πr T cosα = weight of the liquid column below the meniscus (1) The weight of the liquid column is calculated as follows: If h is the vertical height of the capillary ascent from the bottom of the meniscus to the horizontal part of the free surface, then the volume of this column of liquid, V = pr 2 h Rise of liquid in a capillary and hemispherical meniscus of liquid If the bore of the capillary tube is very fine, the meniscus is a hemisphere of radius r and volume u of the liquid in the meniscus as shown in fig = (volume of cylinder of radius r and height r) --- (volume of sphere of radius r ) = π r 2 X r ---. ( ) πr 3 =. πr 3 So the total volume V of the liquid column is given by Page 1 of 6

2 V + = r 2 h + πr 3 = πr 2 ( h + r) The weight of the liquid column = πr 2 ( h + r) ρ g (2) Hence for equilibrium of liquid column from (1) and (2) 2πr. T cosα = πr 2 ( h + r) ρ g Or T = r ( h + r) ρ g / 2Cosα (3) Equation (3) holds good for any liquid. For water, since a is very small, Cos α = 1 and hence the formula becomes T = r ( h + r) / 2 x pg (4) Procedure: (1) Take a fine motion adjustable stand whose height can be increased or decreased slowly. Place on it flat bottom beaker (dish). Fill the beaker with tap water free from dirt and grease (do not use distilled water as it is generally greasy) such that the free surface of water stands a little below the edge of the beaker. (2) Choose three capillary tubes of diameters ranging from 0.1 mm to 0.5 mm. (3) Fix them on a metal plate with the help of a rubber bands. Set the glass plate vertically over the beaker. Fill the beaker upto the brim with water. Hold the plate containing water by holding it in a clamp stand. Adjust the position of the adjustable stand in such a way that the ends of the capillary tubes are well within water. (4) Mount a fine pin parallel to the capillary tubes with its tip just above the water surface. Page 2 of 6

3 (5) Calculate the least count of travelling microscope. (6) Raise the microscope to a suitable height, keep its axis horizontal and view the water meniscus in the first tube, through the microscope. Make fine adjustment so that the horizontal cross wire just touches the lowest point of the concave meniscus (which looks inverted). Take the reading of the microscope. (7) Now lower the microscope till the horizontal cross wire is midway between lower pointed end of the needle and its image in water. (This gives the position of the free surface of water).record this reading of the microscope also. The difference between these two readings gives the height of the water column (capillary rise) in tube. (8) Repeat the above steps with the other two tubes also and record the corresponding observations. Not e the temperature of water with the help of a thermometer. (9) To find the radius r of a capillary tube, put an ink mark at the point where the meniscus stood and cut it at this point with sharp edge of a blade or a sharp file. Never break the tube by bending as it would cause and uneven fracture. To get an even and clear fracture scratch the tube at ink mark by a sharp file and apply tension along length of the tube. Measurement of Diameter: Fix the cut tube horizontal on the glass strip. Focus the microscope on the cut out end of the capillary tube and measure its internal diameter in two mutually perpendicular directions. Also find out internal diameters of other two tubes in the same way.record the observations as detailed below. Page 3 of 6

4 Observations: Determination of h. Least Count of the microscope (a) cm. For Capillary Rise tube No. of Capillary tube used Readings of meniscus h1 (cm) MSR (cm) VSR (cm) TR (cm) Readings of tip of pin touching free surface of water h2 (cm) MSR (cm) VSR (cm) TR (cm) h = h1 h2 (cm) Page 4 of 6

5 Measurement of diameter No. of tube Reading along one diameter AB (cm) One end Diameter d1 (cm) Other end Reading along perpendicular direction EF (cm) Diameter d 1 (cm) One end Mean Diameter cm Other end Mean radius r = d/2 cm 1. Temperature of water (θ ) = C 2. Density of water at θ 0 C, ρ = g cm -3 Calculations: Substitute the value of h and r for each capillary and calculate T for observation of each tube by using the relation: T = ρge ( h+ ) Mean value of T = Nm -1 at θ 0 C = dynes/cm = x10-3 N/m at θ 0 C Result: The surface tension of water at q deg C as determined by the capillary rise method = N/m. Precautions: (1) Capillary tube should be clean and liquid should be free from contamination. This can be ascertained by drawing tubes just before the experiment from soft glass tubing which are first rinsed with caustic soda, then with nitric acid, then with considerable quantity of tap water to remove all traces of nitric acid. (2) The capillary tube should be set vertical. (3) The top of the tubes must be open and not blocked with wax or something else. (4) As the surface tension is very sensitive to the changes of temperature, hence the temperature must be recorded in the beginning and also at the end. Page 5 of 6

6 (5) The water level in the should be a little above its edge so that does not come in the way of observation. (6) The dish should be first washed with the acid so that when water is poured into it there are no grease traces in it. (7) The lower tip of the pin should be just above the water surface but should not touch it. (8) The horizontal cross wire should touch the lower meniscus before taking the reading. Page 6 of 6

7 Object: To determine the moment of inertia with the help of flywheel. Apparatus: Fly wheel, slotted weights, stop clock and vernier calliperse. Formula: The moment of inertia I of the flywheel is given by- Where m = Mass suspended at the end of string, r= Radius of the axle, n1 = No. of revolutions made by the flywheel before the mass its detached from wheel, n2= No. of revolutions made by flywheel to comes rest after the mass is detached. t= time taken by the wheel in the revolutions, g= Acceleration due to gravity Procedure: (1) Attach a mass m to one end of a thin thread and loop is made at the other end which is first end to the peg. (2) The thread is wrapped evenly round the axle of the wheel. (3) Allow the mass to descend slowly and count the no. of revolutions n1 during decent. (4) When the thread has unwound itself and detached from the axle after n1 turns, start the stop clock. Count the no. of revolutions before the flywheel comes to rest and stop the stop clock. Thus n2 and t are known. Page 1 of 3

8 (5) With the help of vernier calliperse, measure diameter of axle at several points. Thus find r. (6) Repeat the experiment with three different m. (7) Calculate the value of I using the given formula. Observations: S.N Total load applied m gm. Table for determination of n1, n2 and t No. of revolutions of No. of revolutions Time flywheel before the of flywheel comes t second mass detached n1 to rest after mass detached n2 Table for determination of radius of axle S.N. Main scale Vernier Total Mean Mean reading scale reading diameter radius cm. reading cm. cm. cm Calculations: Page 2 of 3

9 Result : The moment of inertia of the flywheel is I = gm cm 2 Percentage error: X 100 Precautions: (1) Thread should be uniform winding on the scale. (2) The string loop should be loose. (3) Friction should be made small by greasing the ball bearings. (4) The diameter of the scale should be measure at various point. (5) Mass should be freely. Page 3 of 3

10 Object: To determine the focal Length of a convex lens by u-v method. Apparatus: Convex lens, Two Pin, Optical bench. Theory: The focal length of the lens is given by- Where V= image distance U = object distance Here image distance V is positive, Object distance U is negative, therefore- F = Procedure: (1) Mount the appropriate combination of lens L, Pin P and Pin Q on an optical bench.(see fig last page) (2) Fix lens and pin P at some whole number on the bench such that the distance between L and P is >2F i.e. U>2F. (3) If we look from the opposite side of lens, we will get an inverted, diminished and real image of P. (4) Adjust the position of Pin Q such that pin Q and the image of pin P appear to touch each other. By moving pin Q forward and backward remove parallax between Q and the image P. Note the position of Q, slightly disturb and again remove parallax. Repeat this three times. This is one set. (5) Keeping Pin P fixed, change the position of lens by 2-3 cm and repeat the above steps. This is second set. Take such three sets. Page 1 of 3

11 Observation Table: S.N. 01 Position of object pin u cm Position of Lens (L) cm. Position of image pin v cm u+v F = Calculation: F1= cm. F2= cm F3= cm Mean value of focal length F = cm. Result: The focal length of given lens F = cm. Precautions: 1. Use convex lens of smaller focal length an assure that the combination behaves as a convex lens. 2. Pins should be sharp and pointed one. 3. If the focal length of the combination is large, use only plane mirror method. Page 2 of 3

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13 Object: To find out the unknown resistance by meter bridge. Apparatus: Meter Bridge, Galvanometer, Resistance Box, One way key, Resistance wire. Theory: Meter Bridge is simple apparatus based on the principle of Whetstone s bridge. It consists of one meter long wire and connected in between two thick aluminum strip on lower side of wooden stand. A meter scale with jockey is fixed along it. A thick aluminum strip is mounted on upper side of wooden board. The terminals are mounted on thick aluminum plate and on wooden board for making connections. Measurement of Unknown Resistance: The unknown resistance (X=R) is inserted in the gap P and a resistance box RB is placed in gap Q as shown in Fig. The terminal B is joined to one end of the galvanometer whose other end is joined to a jockey which slides along the wire AC. A battery eliminator is connected in between A and C through one way key (K). Now close the key (K) to complete the circuit. A known resistance Q is inserted from the decade resistance box X by proper adjustment the knob of the resistance box and the jockey is moved to a point, such that on pressing it there is no deflection in the galvanometer. In this position B and D are at the same potential. Since the wire AC is of uniform cross-section, the ratio of the resistance of arm AD to the resistance of arm DC is the same as the ratio of the length AD to the length DC. Page 1 of 5

14 Therefore = = Where k is the resistance of wire per unit length. If length AD = l cm, then length DC = (100-/) cm because AC = 100 cm. = Q x = Q x Since l can be measured and R is known, X can be determined. PROCEDURE 01 Make the circuit diagram as shown in Fig.. 02 Arrange the meter bridge and the various components; the resistance wire, Decade Resistance Box (R.B.), galvanometer, Battery Eliminator as shown in Fig.. 03 Clean the ends of the connection wires by rubbing with sand paper. 04 Ensure that the wire used for connecting the jockey to the galvanometer is sufficiently long. 05 Introduce a suitable resistance say, R = 10Ω from the Decade Resistance Box. Close the key K to complete the circuit. 06 To check the circuit, press the jockey near left and of the wire at point A and note the direction of deflection of the galvanometer needle. Now shift the jockey to other extreme end point C of the wire and note the direction of deflection of the needle of the galvanometer. The directions of deflection should be opposite in the above two cases. If the deflection is on one side only then there is some fault in the circuit. Check up or seek help of your teacher and rectify the fault. 07 Now choose an appropriate value of R from the Decade Resistance Box such that there is no deflection in the galvanometer when the jockey is nearly in the middle of the wire. Take two readings for the length of the wire for null deflection; one while moving the jockey from left to right and the other from right to left, i.e. in the reverse direction. Then take the mean value of l and determine (100- l ) for mean value of X. 08 Repeat the above steps Four times more, by selecting the suitable values of R for the null point to fall approx. between 30 cm to 70 cm. 09 Record your observations in Table. Page 2 of 5

15 OBSERVATIONS No. of Observation Resistanc e R Position of balance point D When l is Increasi decreasi mea ng ng n Lengt h AD = l Length DC = (100- l ) X = ( 1 /100-l ) R (Ohm) (cm) (cm) (cm) (cm) (cm) (Ohm) 01 X1= 02 X2= 03 X3= 04 X4= CALULATIONS : Mean value of resistance, X = =.. ohm. RESULT: The value of unknown resistance as determined by using a meter bridge is found to be. ohms. Page 3 of 5

16 Precautions: 1.The connections should be neat, clean and tight. For this purpose the ends of the connecting wires and the terminals of various accessories should be rubbed and cleaned with a sand paper. The apparatus should be arranged first according to the arrangement diagram then the connection should be made accordingly. 2. The key of the eliminator should be closed only when the reading is being taken and opened immediately after that of minimize the error due to change of resistance by heating. 3. While moving to and fro to locate the balance point, the jockey should be lifted/sided again and again and should not touch the wire throughout. 4. While finding out the balance point, the sliding contact should not be pressed too hard, otherwise the uniformity of the wire will be damaged. 5. The key of the eliminator should be closed first before pressing the jockey on the bridge wire, but for stopping the current in circuit, reverse order should be followed. Page 4 of 5

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18 Object: To verify Newton s law of cooling. Apparatus: Copper Calorimeter, Stirrer, A wooden lid having a hole in the middle, Thermometer, Stop Watch, Beaker, Hot water about 80 0 C. Description of apparatus: The law of cooling apparatus has a cylindrical copper vessel containing a stirrer of the same material. It is provided with a non conducting lid having two holes. The sensitive thermometer is passed through one hole. Through the other hole the stirrer is passed. Newton s law of cooling: The rate at which a hot body loses heat is directly proportional to the difference between the temperature of the hot body and that of its surroundings and depends on the nature of material and the surface area of the body. This is Newton s law of cooling. Procedure: Fill about 2/3rd of the copper calorimeter containing stirrer with hot water of about 80 C. Place the calorimeter inside the cylindrical copper vessel. The space between the cylindrical copper vessel and calorimeter is filled with cotton to avoid heat loss. Page 1 of 3

19 Close the wooden box with its lid. Suspend the thermometer inside the hot water in the calorimeter. Stir water continuously to make it cool uniformly. When the temperature of hot water falls to 80 C, start the stop watch. Note the temperature reading at every five minutes. Continue the time temperature observation till the temperature becomes constant. Plot a graph between time along X-axis and temperature along Y-axis. This graph is called the cooling curve. The graph is an exponential curve and it shows that the temperature falls quickly at the beginning and then slowly as the difference of temperature goes on decreasing. This verifies the Newton s Law of cooling Observations: S. N. Time for cooling, t (min.) Temperature of water in calorimeter, T( o C) Page 2 of 3

20 Calculations: Now, plot a graph between time (t) and temperature (T), taking time along X axis and temperature along Y axis. Results: The cooling curve is plotted. The temperature falls quickly in the beginning and then slowly as the difference of temperature goes on decreasing. This is in agreement with Newton s Law of cooling. Page 3 of 3

21 Objective: To Verify Ohm s Law. Apparatus Required Ohm s law experiment kit, patch chords Theory: According to the ohm s law, if physical conditions of resistance remains unchanged, the potential difference across the ends of resistance is directly preoperational to the current flowing through it. It means V I or V = IR Where, R is the resistance. If potential difference is measured in volt and current I in ampere, then resistance R is measured in ohm. Therefore, to show the current-voltage relation (or ohm s law) it has to be proved that on changing potential difference across the ends of resistance, the change in current is such that ration of V and I remains the same. Formula Used: From the Ohm s law, Resistance R = Ohm Where, V is the potential difference across its ends when current of I ampere is flowing. Procedure: First, connect the circuit. For this connect the ammeter in series with power supply & connect the voltmeter in parallel with power supply. Determination of values of resistances individually: 1. For this, connect the terminal E & F of 100 ohm with terminal A & B. Now verify the Ohm s law and find the value of the given resistance.(see circuit diagram last page).s 2. Repeat this method for 1K ohm and find the values of given resistances. Page 1 of 4

22 Observations: S.N. Voltmeter reading V (in volt) Ammeter reading I (in ampere) Resistance R Mean resistance R =. ohm Calculations : Calculate the value of resistance R by calculating the value of V / I for each observation and find its mean value Now plot a graph by taking V on & - axis and I on X-axis which is a straight line.take two points P and Q on the graph and note down the corresponding values on X and & axis. Now calculate slope of straight line by using formula From Graphical Method : V 2 V 1 Resistance R = = I 2 I 1 Result:- 1. From observation table, it is clear that on increasing current of resistance, the potential difference across its ends also increases. Page 2 of 4

23 2. Ratio between potential difference and current remains the same. Hence, the potential difference across the ends of resistance is directly proportional to current flowing through it. This is Ohm s law. 3. The graph plotted between current I & potential difference V is straight line. Hence, it is proved that the potential difference across the ends of resistance is directly proportional to current flowing through it. This is Ohm s law. 4. The value of given resistance =.ohm Permissible Percentage Error: From formula R = V / I, the permissible percentage error in value of R is ( R) X 100% = =.% Where, V = least count of voltmeter. Precautions: I = least count of ammeter. 1. Current should not flow for longer duration. 2. After completing circuit, it should be checked that the supply is not short circuited. Page 3 of 4

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25 Object: To determine the refractive index of prism (i-d) curve. Apparatus: Prism, a drawing board, drawing paper, drawing pins, office pins, half meter scale and protractor. In the figure ABC is the base of prism. PQ = Incident ray, QR = Refracted ray RS = Emergent ray, i1 = Angle of incidence I2 = Angle of emergence, Angle of deviation r1 = Angle of refraction, NM and N M = Normal s Formula : A m Sin( ) 2 A Sin( ) 2 Where A= Angle of prism, m = Angle of minimum deviation, =refractive index of the material of prism. Page 1 of 5

26 Procedure: (A) Determination of Refractive Angle of Prism : 1. Take a sheet of white paper, fix it over the drawing board by drawing pins at four corners. Draw a straight line MN on the paper as shown in the fig. At the middle of this line, put a mark. O and on either side O marks two points L and T. Draw lines perpendicular to line MN from the points L, O and T. 2. Place the prism ABC, in such a way that its base BC touches the line MN and A falls on the line OK. Draw the outline of the prism. 3. Fix two pins P1 and P2 on the line I1 L. These pins should be about 8 to 10 cm apart. Observe the reflected images of the pins P1 and P2 at the face AB. Place two pins P3 and P4 such that they exactly cover the images of pins P1 and P2. Take out the pins and mark their positions (made by pointed ends). Join the positions of pins P3 and P4 by the line QR1. This represents the reflected ray for the incident ray I1Q. 4. Remove the pins and fix two pins P1 and P2 on the line I2T. Adopting similar procedure as in step 3 obtain the reflected ray Q R2 for the incident ray I2Q. 5. Produce the reflected rays QR1 and Q R2 back ward so as to meet at the point M which line on the line OK. Measure the angle QMQ, which is equal to 2A. Half of this angle gives the angle of prism. (B) Finding out the angle of deviation corresponding to angle of Page 2 of 5

27 Incidence. 6. Take out the white paper from the drawing board and turn it over. Again fix this sheet on the drawing board with the drawing pins at its four corners. 7. Draw a long line 00 on the paper. Take a number of points M1, M2, M3.. etc. each about 10 cm apart. Draw perpendicular lines M1, N2, M2N2, M3N3 etc. from these points as shown in the fig. 8. Draw lines I1M1, I2M2, I3M3, etc. making as angle of 30 0, 35 0, etc. respectively with the respective normal s 1with the help of protractor. Produce these lines as M1T1, M2T2, M3T3. etc. 9. Fix two pins P1 and P2, 10 cm apart, on the first incident line I1M1 Place the glass prism with face AB touching the line OO. Look for the images of the pins P1and P2 from the refracting face AC. Fix two more pins P3 and P4 again 10 cm apart, so that they may cover the images of P1 and P Remove the pins and locate the positions of their pointed ends by encircling them with small circles. Join the points P3 and P4 and produce it backwards so that it may meet the line of incident ray. <SD1T1 gives the angle of deviation by putting protractor at D Repeat the procedure from step 7 to 10 for other angles of incidence 35 0, 40 0, 60 0 and measure the angles of deviation for these angles. Page 3 of 5

28 Observations: (A) Angle of Prism S. No. < 2 A < A Mean < A (B) Angle of deviation Calculation: S. No. Angle of Incidence Angle of Deviation m A m Sin( ) 2 A Sin( ) 2 Result : The refractive index of the material of the prism is found = (i d) Curve: Page 4 of 5

29 Percentage Error = X 100 Precautions: 1. The pins should be fixed vertically. 2. The angle of incidence should not be taken less than The parallax should be removed with the base not by the heads. 4. The prism should be clean. 5. )curve should be smooth. Page 5 of 5

30 Object: To determine the refractive index of prism by using spectrometer. Apparatus: Spectrometer, Prism, Mercury source and reading lens. Formula Used: The refractive index of the prism is given by A Sin( Sin( Where, A = Angle of the prism, m = Angle of minimum deviation m ) 2 A ) 2 Procedure: Measurement of the angle of prism 1. Determine the least count of the spectrometer. 2. Place the prism on the prism table with its refracting angle A towards the collimeter and with its refracting edge at the center. In this case some of the light failing on each face will be reflected and can be received with the help of telescope. 3. The telescope is moved to one side to receive the light reflected from the face AB and the cross wire are focused on the image of the slit. The readings of the two verniers are taken. Page 1 of 4

31 4. The telescope is moved in other side to receive the light from the face AC and again the crosswire are focused on the image of the slit. The readings of two vernier are noted. 5. The angle through which the telescope is moved or the difference in the two positions gives twice the refracting angle A of the prism. Therefore half of this angle gives the refracting angle of the prism. Observation Table: Table for angle of the Prism S.N. Vernier Telescope reading Telescope reading 2A = Mean A for reflection from for reflection from a b 2A deg First face Second face deg. deg M.S. V.S. Total M.S. V.S. Total deg. a deg. b deg. deg. V1 V2 MEASUREMENT OF THE ANGLE OF MINIMUM DEVIATION 1. Place the prism so that its centre coincide with the centre 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. 2. The spectrum is seen through the telescope is adjusted for minimum deviation position for a particular colour (wavelength) in the following way: - Setup telescope at a particular colour and rotate the prism table in one direction, of course the telescope should be moved in such way to keep the spectral line in view. By doing so a position will come where the spectral line recedes in the opposite direction although the rotation of the table is continued Page 2 of 4

32 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 reading of the two verniers. 3. Remove the prism table and bring the telescope in the line of the collimeter. See the slit directly through telescope and coincide the image of slit with vertical crosswire. Note the readings of two verniers. 4. The difference in minimum deviation position and direct position gives the angle of minimum deviation for that colour. 5. The same procedure is repeated to obtain the angles of minimum deviation for other colors. Table for angle of minimum deviation m S.N. Color Vernier (Dispersed image) Telescope Deviation Mean Telescope in reading for a b Deviation minimum direct image m deg. deviation position 1. Violet V1 V2 2. Yellow V1 V2 3. Red V1 V2 Result: Refractive index of prism is =. Percentage Error: X 100 Page 3 of 4

33 Precautions: 1. The telescope and collimeter should be individually set for parallel rays. 2. Slit should be narrow as possible. 3. While taking observations, the telescope and prism table should be clamped with the help of clamping screws. 4. Both verniers should be noted. 5. 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. Page 4 of 4

34 Object:To find out volume of given cylinder by screw gauge. Apparatus : Screw gauge, cylindrical rod Theory and Formula: The screw gauge is an instrument used for measuring accurately the diameter of a thin wire and volume of given cylinder. It consists of a U-shaped frame fitted with a screwed spindle which is attached to a thimble. Parallel to the axis of the thimble, a scale graduated in mm is engraved. This is called pitch scale. A sleeve is attached to the head of the screw. The head of the screw has a ratchet which avoids undue tightening of the screw. On the thimble there is a circular scale known as head scale which is divided into 50 or 100 equal parts. When the screw is worked, the sleeve moves over the pitch scale. Pitch of the Screw Gauge The pitch of the screw is the distance moved by the spindle per revolution. To find this, the distance advanced by the head scale over the pitch scale for a definite number of complete rotation of the screw is determined. The pitch can be represented as; Least Count of the Screw Gauge The Least count (LC) is the distance moved by the tip of the screw, when the screw is turned through 1 division of the head scale. Page 1 of 3

35 The least count can be calculated using the formula; Total reading = Main scale reading + (Circular scale reading X least count) Volume of given cylinder = πr 2 h Procedure: 1. Determine the pitch and least count of the screw gauge. 2. Bring the anvil and screw in contact with each other and find the zero error. If there is no zero error, then record zero error nil. 3. Move the screw away from the anvil and place the cylinder and move the screw towards the anvil using the ratchet head. Stop when the ratchet slips without moving the screw. 4. Note the number of divisions on the pitch scale that is visible and uncovered by the edge of the cap. The reading N is called the pitch scale reading(psr) 5. Note the number (n) of the division of the circular scale lying over the reference line. 6. Repeat steps after rotating the cylinder. Record the observations in the tabular column. 7. Find total reading using and apply zero correction in each case. 8. Take the mean of different values. Page 2 of 3

36 Observations Table: 1. Height of the given cylinder h = mm or cm. S.N. Main Scale Reading cm. Circular scale reading coinciding division s no. on (Circular scale X L.C.) cm Diameter D= MSR+(CSR X L.C) (in cm.) 1. a= cm. 2. b= cm. 3. Calculations : Radius of given cylinder r = cm. Volume of given cylinder = πr 2 h Result: Volume of the given cylinder = cm. Precaution: (i) Check the zero error of screw gauge. (ii) If positive zero error is present, first calculate and then subtract it with positive sign from total reading. (iii) If zero error is negative, after calculating subtract it with negative sign from total reading. (iv) Take all observations carefully. Page 3 of 3

37 Object:To find out internal radius of hollow tube by vernier calliperse Apparatus:VernierCalliperse, hollow tube. Description of apparatus:vernier calliperse was invented by a French mathematician Pierre vernier. It is used to measure the length of a rod or diameter of a sphere, the internal and external diameter of a hollow cylinder and the depth of small vessel. The construction of vernier calliperse shown in the figure. It consists of a steel strip graduated in inch.it is called the main scale. There is another strip known as vernier scale which can slide over the main scale, and is graduted with the no. of divisions. The vernier scale can be fixed at any position on the main scale by means of a screw. There are two jaws perpendicular to the main scale. One of the jaw is fixed at the left end of the main scale and other jaw is fixed on the frame of the vernier scale. The lower outsider jaws are used to measure the length or the external diameter of an object and the upper inside jaws are used to measure the internal diameter of a hollow tube. The verniercalliperse provided with along the strip attached at the back of the main scale. The strip is used to measure the depth of any small vessel. Least Count:The least distance which can be measured by an instrument is called the least count of the instrument. Least Count = Total Reading = main Sc. reading + (vernier sc. reading X Least count) Page 1 of 2

38 Procedure: (1) Calculate the least count of the vernier calliperse using the above formula. (2) Bring both the jaws together and see the whether the zero mark of vernier scale coincides with the zero mark of the main scale or not. If they do not coincide, find the zero error by the method. (3) Fix the internal jaws in between the hollow tube and note the main scale reading. (4) Now find the vernier scale reading. For this, note the vernier scale division which coincides with any the main scale division. Multiply this no. of vernier division with the least count to get the vernier scale reading. (5) Find the total reading by adding the main scale and vernier scale readings. (6) From this, subtract the zero error with its proper sign to obtain the correct diameter of the given hollow tube. (7) Repeat the experiment and note the readings at different places along the hollow tube and their mean is obtained and arranged in tabular form. Observation Table: S.N. Main scalereading inch. Calculation: Mean diameter of hollow tube D = Internal radius of hollow tube = cm. Vernier Scale Reading 1. a1= 2. a2= 3. a3= 4. a4 = Total Reading a cm cm. Result: The internal radius of given hollow tube is R = cm Precautions: (i) Check the zero error of verniercallipers. (ii) If positive zero error is present, first calculate and then subtract it with positive signed from total reading. (iii) If zero error is negative, after calculation subtract it with negative form total reading. (iv) Take all the observations carefully. Page 2 of 2