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# Verniers Calipers | Physics Practical XI

**NAME OF EXPERIMENT** **:** TO USE A VERNIER CALIPERS TO DETERMINE THE VOLUME OF THE GIVEN TUBE.

**APPARATUS REQUIRED : **(i) Vernier calipers (ii) Given Tube

**THEORY : **The vernier calipers is a device used for measuring lengths in fractions of a millimeter with greater accuracy as compared to that of ordinary scale . It consists of main scale **(MS)** and vernier scale **(VS)** . The vernier scale **(VS)** slide over the main scale while main scale **(MS)** is fixed.

The vernier constant **(VC) **of the smallest length that can be measured accurately . It is the difference between the values of the smallest division of the main scale **(MS)** and that of the vernier scale **(VS)**. i.e.

**VC = MS – VS (I)**

In general `n`

division of the vernier scale **(VS)** coincide with `n-1`

divisions of the main scale **(MS)** , So –

**(n-1) MS = n VS**

**or, MS – VS = MS / n**

**∴ ****VC = **value of smallest main scale Division **(****MSD) ÷ **Total Vernier Scale Division **(VSD)**

**∴ **Length = MS reading + VS reading * VC ± Instrumental Error

**FOR VOLUME**** :**

Let,

l = length of the tube

d_{1} =external diameter of the tube

d_{2} =internal diameter of the tube

We have ,

external volume(V_{1}) = **π/4 (d _{1})^{2}l**

internal volume(V_{2}) = **π/4 (d _{2})^{2}l**

**∴ **Volume of the tube **(V) = V _{1}-V_{2}**

**∴ V = πl/4*(d _{2}^{2}-d_{1}^{2})**

**OBSERVATION**** : **

**a) **Determination of Vernier Constant (Least Count) of the Vernier Calipers :

Value of `1`

division of main scale = 1mm **(MS)**

**10 VSD = 9 MSD**

** ∴ 1 VSD = 9/10 MSD = 0.9 MSD = 0.9mm(VS)**

**∴ Vernier Constant (VC) = MS – VS = 1mm – 0.9mm = 0.1mm = 0.01cm**

**b)** Measurement of volume :

#### Measurement with vernier calliper

Obs for | No. of Obs | Reading of the | Total
(1) + (3) |
Mean | ||

MS (1) | VS (2) | VS*VC (3) | ||||

Length (l) | 1 | l=…….cm | ||||

2 | ||||||

3 | ||||||

4 | ||||||

5 | ||||||

Ext. Diameter (d_{2}) |
1 | d_{2 }= …..cm |
||||

2 | ||||||

3 | ||||||

4 | ||||||

5 | ||||||

Int. Diameter(d_{1}) |
1 | d_{1} =….cm |
||||

2 | ||||||

3 | ||||||

4 | ||||||

5 |

**∴ **Volume of the tube **(V) **= ** πl/4*(d _{2}^{2}-d_{1}^{2}) = **………

**cm**

^{3}**RESULT**

**:**The volume of the given tube is …… cm

^{3}.

**PRECAUTIONS**** :**

**a) **Ensure that the zero error is worked out properly before actual measurement.

**b) **Donot aapply excess pressure on the bodyheld between jaws.

**c) **All measurement must be done without parallax error.

**d) **Record all the reading in same system preferably in **C.G.S **system .

## Important Questions

## Physics Grade XI viva Question Vernier calliper

**1: What is vernier calipers?**

Ans. It is simple instrument by which length of an object can be measured accurately up to one-tenth of a millimeter or one-hundredth of a centimeter.

**2: What is the use of Vernier Scale?**

Ans. To increase the accuracy of the main scale.

**3: What is least count (L.C.)?**

Ans. The minimum measurement that can be taken by an instrument.

**4: What is the least count of?**

(a) meter scale (b) Stop Watch (c) Vernier Calliper

Ans. The least count of:

(a) meter scale = 0.1 cm or 1 mm.

(b) stop watch = 0.01 sec or 1/100 sec. or according to stop watch.

(c) vernier scale = 0.01 cm or 0.1 mm

**5: What are units of vernier scale?**

Ans. Vernier has not units of its own.

**6: What is the difference in the measurement of one smaller division on the main scale (M.S.) and that of vernier scale** (V.S.)

Ans. (1 smallest Div. on M.S.) – (1 smallest Div. on V.S) = 0.1 – 0.09 = 0.01 cm = Least count.

**7: How the L.C. of a vernier is determined?**

Ans. By using the relation:

L.C. = (Smallest division on Main Scale ) / (Total number of divisions on Vernier Scale)

**8: Will the accuracy of a vernier will increase or decrease if 20 divisions are made in the same length?**

Ans. The accuracy will increase since the L.C. will decrease i.e. Accuracy α = 1 / Least count

**9: Which one is smaller M.S. div. or V.S. div.?**

Ans. V.S. division.

10: 1 division on V.S. = _____ cm.

Ans. 0.09 cm.

10 div. on V.S. = 0.9 cm

1 div. on V.S. = 0.9/10 cm = 0.09 cm

**11: What are the functions of (a) Sliding strip (b) Upper jaws**

Ans. (a) For measuring depth. (b) For measuring the inner diameter.

**12: What is meant by zero error (Z.E.)?**

Ans. The error which arises when zeros of M.S. and V.S. do not coincide upon joining the two jaws.

**13: When Z.E. is positive**?

Ans. The Z.E. is positive when the zero of V.S. is to the right of the zero of M.S.

**14: How we find the corrected reading?**

Ans. Corrected reading = Meaning reading – ( + Z.E.)

**.15: Do you know any use of vernier scale?**

Ans. It is used in spectrometer, barometer, traveling microscope, etc.

**16: What are significant figures?**

Ans. Numbers 0, 1, 2, 3, ……. are called significant figures when they occur. The zero is not a significant figure if it is at the extreme left or extreme right of a number, e.g. 1.02 has three significant figures, but 1.20 has two significant figures.

**17: What is meant by degree of accuracy?**

Ans. It is the measurement estimated by the number of significant figures in the result.

**18: Why is the vernier calipers so called?**

Ans. A French mathematician named Pierre Vernier invented it and it is named after him.

**19: How does temperature affect the length of a cylinder?**

Ans. The length of a cylinder increases with the increase of temperature and decreases with the

decrease of temperature.

**20: What is the unit of volume?**

Ans. In MKS system, the unit of volume is m3. In CGS system, the unit of volume is cm3. In FPS

system, the unit of volume is ft3.