Pre-Lab 1-Vernier Calipers PDF

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Pre-Lab 1: “Vernier Callipers” Aim:

(i) To understand the use of the Vernier Calipers. (ii) To measure the diameter of a small spherical/ cylindrical body. (iii) To measure the dimensions (length, width and height) of the given rectangular block. (iv) To measure the internal diameter and depth of a given beaker/ calorimeter and hence find its volume.

Theory: Vernier Calipers is a device to measure lengths accurate upto 1/10th or 1/20th of a millimetre. It consists of rectangular steel bar having graduations in inches on one edge and in centimetres on the other edge as shown in the Fig. 1. This constitutes the main scale or linear scale. Over this scale slides an auxiliary scale also called as the vernier scale.

Fig. 1

It has two outer measuring jaws A and B. The jaw A is fixed at the end of the rectangular bar towards zero side while the other jaw B is capable of sliding along the edge of the main scale. The inner measuring jaws P and Q are projected in the upper part of the device where P is fixed and Q is movable. The two vernier scales are attached to the movable jaw as shown. The retainer is used to slide the vernier scale on the main scale and also helps to retain the body (externally or internally) across either pair of jaws of the Vernier calipers. When two jaws are put in contact with each other, the zero of the

(a)

(b) (c) Fig. 2 vernier scale should coincide with the zero of the main scale [Fig. 2(a)]. If it is not so, then the device is Page 1 of 8

said to have the zero error. Depending upon whether the zero of vernier scale lies to the right or to the left of the zero of the main scale, the zero error respectively may be positive or negative [Fig. 2(b) and 2(c)]. To calculate the zero error, let m th vernier division be coinciding with any division of the main scale. Then Zero error (e) = m

Least count (L.C.)

Zero correction (c) =

Zero error = -e

(i)

This zero correction is needed to be applied in the which is proportional to the right (or left) shift of the zero of the vernier scale relative to that of the main scale. Thus,

True reading = Observed reading + c

(ii)

For positive zero error, e is +ve so that c will be negative. For negative zero error, e is ve so that c will be positive. Least count calculation: The least count (L.C.) or the vernier constant (V.C.) or the smallest reading which one can obtain with the device can be calculated as follows: The graduations on the vernier scale are such that its n divisions are normally made to coincide with ( n 1) divisions of the main scale. Under such a situation (n or

1) MSD = n VSD 1 VSD =

(n 1) MSD n

Now, vernier constant is the difference between one main scale division and one vernier scale division i.e.

V.C. = L.C. = 1 MSD

1 VSD

 n 1 1 = 1  MSD = MSD n n   Thus,

Vernier constant =

(iii)

One main scale division No. of divisions in vernier scale

Reading Calculations: When an object is between the two jaws of the Vernier Caliper: If the zero of the vernier scale lies ahead of the Nth division of the main scale, then the main scale reading (MSR) is MSR = N

(iv)

If nth division of vernier scale coincides with any division of the main scale, then the vernier scale reading (VSR) is Page 2 of 8

VSR = m

L.C.

(v)

Hence, the total reading is TR = MSR + VSR = N + n

L.C.

(vi)

As an example, let n = 10, i.e. 10 vernier divisions coincide with 9 main scale divisions as shown in Fig. 3(a).

Fig. 3 (a) Since 10 VSD = 9 MSD* 9 1 VSD = MSD ⇒ 10 L.C. = V.C. = 1 MSD – 1 VSD = 1 MSD As

9 1 MSD = MSD 10 10

1 MSD = 1 mm so L.C = 0.1 mm

*Sometimes n may be chosen to be 20 or 50 so that 20 VSD = 19 MSD or 50 VSD = 49 MSD and accordingly the least count changes.

Now let the zero of the vernier lies between 1.2 and 1.3 cm as shown in Fig. 3 (b). One can clearly see that the 6th VSD coincides with an MSD. If we denote the fraction after 1.2 by x, then

Fig. 3 (b)

1.2 + x + 6 VSD = 1.2 + 6 MSD or x = 6 MSD – 6 VSD = 6 (1 MSD – 1 VSD) = 6 L.C. = 0.6 mm The total reading, therefore, becomes (1.2 + 0.6) mm = 1.26 mm.

Determining Volumes: (i) Volume of a Beaker/ Calorimeter Volume of the beaker/ calorimeter = internal area of the cross section This can be expressed as Page 3 of 8

depth

V

D    2

2

d

where 'D' is the internal diameter of beaker/ calorimeter and 'd’ the depth of beaker/ calorimeter. (ii)

Volume of a Sphere This can be expressed as 4  D3   3 2 where ‘D’is the diameter of the sphere. V

(iii) (iv)

Volume of a Rectangular Block This can be expressed as V l b h

where 'l' is length of the block, 'b' the breadth and 'h' the height of the block.

Materials Required:     

Vernier callipers. A spherical body ( it can be a pendulum bob) A solid/ hollow cylinder. A small rectangular metallic block of known mass. A beaker or a calorimeter.

Procedure: 1. Firstly the vernier constant (VC) of the vernier caliper was determined and it was recorded stepwise as in the equation, L.C = 1 MSD 1 VSD. 2. Then the movable jaw was brought in close contact with the fixed jaw and the zero error was determined. This was done three times and the values were recorded. 3. After this, the jaws of the Vernier Calliper were opened and sphere or cylinder was placed between the two jaws and the movable jaw was adjusted, such that it gently gripped the object without any undue pressure on it. At this stage, the screw attached to the Vernier scale was locked. 4. Then the position of the zero mark of the Vernier scale on the main scale was noted and the main scale reading was recorded just before the zero mark of the vernier scale. This reading (N) is called main scale reading (MSR). 5. The number (n) of the Vernier scale division which coincides with the division of the main scale was then noted. 6. The steps 5 and 6 were repeated after rotating the body by 90o for measuring the diameter in a perpendicular direction. 7. The steps 4 to 7 were repeated for three different positions and the observations were recorded. 8. The total reading, for different positions, was found using the equation, TR = MSR + VSR = N + (n x L.C) and the zero correction was applied for each. 9. The mean of the different values of the diameter was taken and was written in the result with the proper unit. 10. To measure the internal diameter of a calorimeter or beaker, the beaker was placed upside down over the internal jaws of the vernier calipers and then the steps 4 to 8 were repeated. 11. To find the ‘Depth’ of the beaker, the metallic strip was moved till it touched the bottom of the beaker. Then steps 4 to 8 were repeated. Page 4 of 8

Observations: 1. Determination of Vernier constant (Least Count ) of the vernier callipers: 1 MSD = 1 mm 10 VSD = 9 MSD 9 MSD = 0.9 mm. 1 VSD = 10 Vernier Constant, V.C. = 1 MSD 1 VSD = (1 0.9) mm = 0.1 mm = 0.01cm. 2. Zero Error (i).........cm, (ii).........cm, (iii)...........cm. Mean zero error (e) =..........cm. Mean zero correction (c) = e =.........cm. 3. Table Dimensions to be measured

S. No.

Main Vernier Scale Scale Reading Reading MSR (cm) VSR (cm)

VSR L.C. (cm)

Diameter of the bob Diameter of the cylinder Length of the cylinder Length of the block Breadth of the block Thickness of the block Internal Diameter of the block Internal depth of the beaker

Calculations: Mean corrected diameter = ------------cm 4 3 r = ---------cm3 = ------m3. Volume of sphere, V 3 Mean corrected length of the block, l =............cm Mean corrected breadth of the block, b = .......cm Page 5 of 8

Total Reading MSR + (VSR L.C.) (cm)

Mean (cm)

Mean corrected thickness of the block, h = .........cm Volume of block, l b h = ........................cm3 = ..........m3 m Density of the block material, = .................kgm 3 V Mean corrected internal diameter, D = ................cm Mean corrected depth, d = ........cm 2

Volume of beaker/ calorimeter, V

 D 3 3   d = ..........cm = ............m .  2

Result (s): The volume of the beaker/ calorimeter is ...........m3. Volume of Sphere=.......................... m 3. Volume of block is ................................m 3 . 3 The volume of the beaker / calorimeter is ...........cm .

Viva-Voce 1) What is vernier constant? (a) least constant (b) angular vernier (c) zero correction (d) least count Ans. (d) 2) What is the function of sliding strip or rod? (a) to measure the width of certain objects (b) to measure the depth of certain objects (c) to measure the radius of certain objects (d) to measure the diameter of certain objects Ans. (b) 3) Why is a slide callipers called a 'Vernier Callipers'? (a) It is the Latin name for 'slide callipers' (b) It was first designed by a French mathematician, Pierre Vernier. (c) Its idea was first conceived at Vernier in southern Germany. (d) None of the above Ans. (b) 4) Which of the following measurements cannot be made by a vernier calliper? (a) Measuring the internal diameter of a cylindrical object or the depth of a vessel. (b) Measuring the height of a tower. (c) Measuring the outer diameter of a spherical or cylindrical object. (d) Measuring the length of an iron nail. Ans. (b) 5) Which of the following is a true statement? (a) Zero correction is algebraically added to the observed reading Page 6 of 8

(b) Zero error is a algebraically subtracted from the observed reading. (c) Negative of zero error is zero correction. (d) All of the above. Ans. (d)

6) Which of the following is incorrect with regard to zero error? (a) It occurs if the zeros of main scale and vernier scale do not coincide. (b) It arises due to wear and tear of the instrument. (c) It is the error in the vernier callipers. (d) It is positive when vernier zero is to the left of main scale and negative if it is to the right. Ans. (d) 7) Least count: metre scale – 1 mm, vernier callipers - 0.1 mm, screw guage and spherometer 0.01 mm. Which has the least accuracy? (a) Metre scale (b) Spherometer (c) Vernier callipers (d) Screw guage Ans. (a) 8) Vernier Constant is given by: (a) V.C.= 1 M.S.D. 1 V.S.D (b) V.C.= 1 M.S.D./1 V.S.D (c) V.C.= 1 M.S.D. + 1 V.S.D (d) V.C.= 1 V.S.D. 1 V.S.D

Ans. (a) 9) Principle of vernier callipers: (a) N main scale division = (N 1) vernier scale divisions. (b) N vernier scale division = (N 1) main scale divisions. (c) N main scale division = N vernier scale divisions. (d) N vernier scale division = (N/2) main scale divisions. Ans. (a)

10) A student used a vernier caliper to measure the length of his pencil. He found that the main scale showed a reading of 8.3 and vernier scale coincides with 5th position to the main scale. What was the correct measurement of the length of the pencil? (a) 8.8 (b) 8.5 (c) 8.35 (d) 8.3 Ans. (c)

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11) The diagram below shows the part of a vernier caliper used to measure the diameter of a soft drink can. What is the reading shown?

(a) 6.44 (b) 6.47 (c) 6.34 (d) 6.37 Ans. (c)

12) During the measurement of the inner diameter of a measuring jar, Arun got the reading as follows. What is the reading shown?

(a) 3.03 cm (b) 3.5 cm (c) 3.54 cm (d) 3.34 cm Ans. (d)

Resources: 1. Books B.Sc. Practical Physics, C. L. Arora, S. Chand & Co. An advanced Course in Practical Physics, D. Chattopadhyay and P. C. Rakshit, NCBA. 2. Websites http://www.wikihow.com/Use-a-Vernier-Caliper https://www.youtube.com/watch?v=VOar5f3LfZs http://www.technologystudent.com/equip1/vernier3.htm

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