Aim: To determine i) The volume of the given cylinder by measuring its length and diameter

ii ) The volume of the given sphere by measuring its diameter.

Apparatus : Vernier Calipers,Cylinder and sphere.

Description of Vernier Calipers: A Vernier calipers consists of mainly two parts i) A 2cm wide 15cm long rectangular metal strip .The left end bottom side of this strip consists of a fixed jaw 1 (A) and at the same end jaw 2(C) at the top of this strip. On the strip a scale (5)is graduated in Inches along the upper edge and another scale(4) is graduated in Centimeters along the lower edge. This is called Main Scale ‘S’ .

ii) A metal frame V called vernier slides over the Main Scale ‘S’ . At the bottom of this frame V a button 8(P) is attached,which helps to fix this vernier at any desired place on the main scale.This verier frame consists of jaw1 (B) at the bottom and a jaw 2(D) at the top .Two scales are graduated on this frame corresponding to two scales on the Main Scale ‘S’. The two scales 6 and 7 on the vernier are called Vernier scale.Vernier scale consists of equal number of divisions. When we move vernier frame over the main scale, a thin strip (3) will be projected out.The projection will be exactly equal to the distance between Jaws 1(AB) i.e the thickness of the object between jaws.

The lower jaws 1,1(AB) are used to measure the thickness or external diameter of the tubes,cylinders or spheres.

The upper jaws 2,2 (CD) are used to measure the inner diameters of hallow bodies like tubes or holes.

The thin strip ( 3) is used to measure the depth of the objects like test tubes.

**Theory** : Principle of vernier calipers – **N divisions on the vernier scale is equal to (N-1) divisions on the main scal**e.

N V.S.D = (N-1) M.S.D

1 V.S.D = M.S.D

Least count (L.C) of vernier calipers : Minimum length or thickness measurable with the vernier calipers is called its least count.

Least count (L.C) = 1 M.S.D – 1 V.S.D

L.C = 1 M.S.D – M.S.D

L.C = 1 M.S.D [ 1-]

L.C = =

Where S is the value of one Main scale division and N is the number of equal divisions on the vernier scale.

**Procedure** : First we have to determine the least count count of the given vernier calipers.

To determine the volume of the cylinder we have to determine a)the length of the cylinder and b) radius of the cylinder and substituting these values in the equation for the volume of the cylinder we can calculate it.

**a) ****To determine the length of the cylinder** : Given cylinder is held gently between jaws 1,1 of the vernier calipers.The reading on the main scale just before the zero of the vernier is noted.This is called Main scale reading (M.S.R).The number of division (n) on the vernier which coincides perfectly with any one of the main scale divisions is noted.This is called vernier coincidence (V.C).The vernier coincidence (V.C=n) is multiplied by least count to get the fraction of a main scale division.This is added to the main scale reading (M.S.R) to total reading or total length of the cylinder.

Total reading = M.S.R + ()

Take the readings,keeping the cylinders between jaws 1,1 at different positions.Post the values of M.S.R and vernier coincidence (n) in the table.Take at least 5 readings, get the average of these 5 readings which is mean length(*l *)of the cylinder.

**b)To determine the diameter of the cylinder **: Place the cylinder diametrically between the jaws 1,1 of the vernier calipers, as in the above case post the values of M.S.R and vernier coincidence (n) in the table. Take at least 5 readings, calculate the average of these readings which gives the mean diameter ( d=2r ) of the cylinder.

**c) To determine the volume of the cylinder** :Substituting the values of mean length (*l *) of the cylinder and mean diameter ( r) of the cylinder which is already determined, in the formula V = .

**d)To determine the diameter of the sphere** : The given sphere is held firmly between jaws of the vernier calipers, in such a way the points where the jaws are in contact with sphere should be the two extremes of the chord of the cylinder.Post the values of the M.S.R and vernier coincidence (n) in the table . Take at least 5 readings, calculate the average of these readings which gives the mean diameter (d=2 r ) of the sphere.

**e)****To determine the volume of the sphere :**Calculate the radius of the sphere r = d/2 .Substitute the value of mean radius (r) in the formula of the volume of the sphere V = .

**Precautions to be taken while doing the experiment **: 1) Take the M.S.R and vernier coincide every time without parallax error. 2)Record all the reading in same system preferably in C.G.S system. 3) Do not apply excess pressure on the body held between the jaws. 4) Check for the ZERO error.When the two jaws of the vernier are in contact,if the zero division of the main scale coincides with the zero of the vernier scale no ZERO error will be there.If not ZERO error will be there, apply correction.

**Observations**:** **

**I) Least count of Vernier calipers :**

a) Value of 1 Main scale division = 1 M.S.D = S = …….. cm,

b) Number of divisions on the vernier scale N= ……… cm,

Least count L.C = = ………. cm.

c) Zero error =x ( positive error)

**II) Volume of the Cylinder** :

**a)Length of the cylinder** :

S.No | M.S.R acm | Vernier Coincidence (n) | Fraction b=(n-x)*L.C | Total Reading (a+b) cm |

1. | ||||

2. | ||||

3. | ||||

4. | ||||

5. |

Average length of the cylinder *l* = ……… cm.

**b) Diameter of the cylinder** :

S.No | M.S.R acm | Vernier Coincidence (n) | Fraction b=(n-x)*L.C | Total Reading (a+b) cm |

1. | ||||

2. | ||||

3. | ||||

4. | ||||

5. |

Average diameter of the cylinder d = 2r = …………. cm,

Mean radius of the cylinder r = d/2 = ………….. cm,

Volume of the cylinder V = .

**III ) Volume of the sphere** :

**a) Diameter of the sphere** :

S.No | M.S.R acm | Vernier Coincidence (n) | Fraction b=(n-x)*L.C | Total Reading (a+b) cm |

1. | ||||

2. | ||||

3. | ||||

4. | ||||

5. |

Average diameter of the sphere d = 2r = …………. cm,

Mean radius of the sphere r = d/2 = ………….. cm,

Volume of the sphere V = .

**Result** : 1. Volume of the given cylinder V= ………..

2.Volume of the given sphere V= ……….. .

Watch this vedio :

**Review Questions – Vernier calipers.**

During practical examinations the examiner can shoot any question related to the experiment you are doing.Here I will try to answer few Frequently asked questions by examiner.

1Q: What is the advantage of vernier calipers over a regular scale graduated in millimeters?

Ans: We can measure up to a millimeter with regular scale which is graduated in millimeters, Where as with a vernier calipers with 10 equal divisions on the vernier scale we can measure up to 1/10 (0.1) mm accurately.

2Q:What is the principle of vernier ?

Ans: (N-1) main scale divisions = N divisions on vernier scale,

(N-1) M.S.D = N V.S.D is the principle of vernier.

3Q:What do you mean by least count of vernier calipers?

Ans: The difference of 1 M.S.D and 1 V.S.D is called least count of a vernier calipers. (or) The minimum

length which can be measured by a vernier calipers is called its least count.

4Q:What is the use of lower jaws of a vernier calipers?

Ans: The lower jaws or used to measure the thickness of object,outer diameters of tubes,spheres and cylinders.

5Q:What is the use of upper jaws?

Ans: The upper jaws of the vernier calipers are used to measure the inner diameters of rings,tubes and inner diameters of hallow cyliders , hallow spheres.

6Q:What is the use of the thin strip moving behind the main scale?

Ans: The strip is used to measure the depths of the tubes and level of the liquid inside tubes or jars.

7Q:Two different vernier calipers have different number of equal divisions on their vernier scales i) 10 equal divisions ii) 50 equal divisions . Which can measure more accurately.

Ans: The least count of the I vernier calipers = S/N = =0.1mm

The least count of the II vernier calipers = S/N = =0.02mm.

That is the II vernier calipers with 0.02mm of L.C can measure up to 0.02mm accurately.Hence the accuracy of II vernier calipers in more than I vernier calipers.

8Q:What is the ZERO error of a vernier calipers?

Ans:When two lower jaws of the vernier calipers are in contact, if the zero division of main scale does not coincide with the zeroth division of vernier scale, such vernier calipers will have zero error.

9Q: What is the formula of least count?

Ans: Least count L.C = .

10Q:What is the formula to calculate the volume of the cylinder?

Ans: Volume of the cylinder V = . , where r = radius of the cylinder and *l = *length of the cylinder.

*11Q:*What is the formula to calculate the volume of a Sphere?

Ans: Volume of the Sphere V = , where r = radius of the sphere.

12Q:What is the formula to calculate total reading with a vernier calipers?

Ans: Total reading = M.S.R + .

13.How many types of Zero errors will be possible in vernier calipers?

Ans: Two types of Zero errors are possible in vernier calipers they are i) Negative Zero error ii) Positive Zero error

14. What is Positive zero error,how do we correct such an error in a vernier calipers?

Ans:When two lower jaws of the vernier calipers are in contact, if the zero division of main scale does not coincide with the zeroth division of vernier scale and the zero of the vernier is to the right of zero of main scale such an error is called Positive Zero error.So,the zero correction should be subtracted from the reading which is measured.

Ex:When two lower jaws of the vernier calipers are in contact, if the zero division of the vernier is to the right of zeroth division of main scale and if the vernier coincidence is 1.Then the correction is subtraction i.e Total Reading –

15.What is Negative zero error,how do we correct such an error in a vernier calipers?

Ans:When two lower jaws of the vernier calipers are in contact, if the zero division of main scale does not coincide with the zeroth division of vernier scale and the zero of the vernier is to the left of zero of main scale such an error is called negative Zero error.So,the zero correction should be added to the reading which is measured.

Ex:When two lower jaws of the vernier calipers are in contact, if the zero division of the vernier is to the left of zeroth division of main scale and if the vernier coincidence is 8.Then the correction is addition i.e Total Reading +

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What happens if instead if N-1 divisions, the N divisions of my vernier calipers divides N-2 or N-3 divisions on the main scale? Is it possible? what changes should we make to find the least count? which caliper would be more accurate?

Hi,

PIYANKA,

As you said if (n-2) M.S.D = n V.S.D

Then I V.S.D = {(n-2)/n} M.S.D

L.C = 1 M.S.D – 1 V.S.D = 1mm – {(n-2)/n} mm = 2/n if n =10

L.C = 2/10 = 0.2 mm

i.e when (n-1) divisions are changed to (n-2)divisions least count is increased from 0.1mm to 0.2mm

i.e the accuracy of the vernier calipers is decreased.

so, if (n-3) M.S.D s are divided in to n equal divisions on vernier scale the L.C further increases and the accuracy further decreases.

Hope this explanation will clarify your doubt.

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Thanks for ur explanation. Thank u…

if n divisions on MS are divided into N-1 divisions on VS, what happens to LC?

Why only 49 MSD are made into 50, why not 39 into 40 or 79 into 80?

If (n-1) divisions of MS are divided in to n divisions on VS then the least count will be positive L.C = 1 M.S.D – 1 V.S.D, where as if n divisions of MS are divided in to (n-1) divisions on VS then the LC of the Vernier Calipers will be negative(such device doesn’t exists)

you can manufacture vernier calipers by dividing 49 MSD are made into 50 VSD or 39 MSD in to 40VSD ………………. with different Least Counts.

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thanx for the information its very simple nd easy to enter in to our minds. it would be much better if u put information regarding positive and negative errors… thax alot

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what is the defination of vernier principle

It really helped me a lot. Thank u sooooooooooo much and I kindly request from u to insert more prctical questions with answers.

how to change least count of a vernier caliper?

L.C = S/N

S= 1 M.S.D ; N= No of equal divisions on vernier scale.

Now for example N=10 then the L.C = 1/10 =0.1 M.S.D or 0.1mm (if M.S.D = 1mm)

If N=9 then the L.C=1/9 M.S.D or 1/9 mm (if M.S.D = 1mm)

like that you can change the least count of vernier calipers by changing the no. of equal divisions on vernier scale.

you can manufacture vernier calipers by dividing 49 MSD are divided into 50 VSD or 39 MSD in to 40VSD ………………. with different Least Counts.

Hope my explanation clarifies your doubt.

Why is it called Vernier calippers?

Respected gyaunnrraje, How to measure inches dimension on vernier caliper?

Respected gyaunnrraje, what are the smaller units of inches?

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Your answers have best clarifications.

what do you mean by 1 M.S.D .if i have a vernier caliper.having M.S in cm.then 1M.S.D will b 1cm or 0.1cm?????????

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Why is it called a vernier caliper?

If you have a vernier calipers in cms each division will be 1mm or 0.1cm .Hence 1M.S.D(1MainScaleDivision ) will be equal to 1mm

3Point Vernier calipers is used to measure the diameters of round objects or milling tools.

thanks ur infermetion

Dear Sir, i have a confusion about vernier calliper. why we multiply least count with the division of vernier scale coincides with main scale, in order to add it with the main scale reading? plz help me out.

Hi, Aftab, The product of vernier coincidende and least count gives the fraction.When we add this fraction value to Main scale reading we get total length of the object

up to 0.1mm accuracy.Hope this explanation will convince you.

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can you tell how to apply correction factor

Hey..Just got a doubt about vernier calliper..

What does it mean by Zero error and Zero corrections..??

For answer to your question,please go through through the review question no’s 8,14&15 in Vernier calipers

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Very well compiled information about the vernier calipers.But, in Q 15 about the negative Zero Error ….

Ex:When two lower jaws of the vernier calipers are in contact, if the zero division of the vernier is to the left of zeroth division of main scale and if the vernier coincidence is 8.Then the correction is addition i.e Total Reading + 8

I think the correction should be Total Reading + (10-8) …if the Vernier coincidence is 8

i.e. the correction is Total Reading + 2

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add de

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normally a vernier caliper has a minimum scale of 0.1mm. but i have heard there some caliper which have another minimum scales which is below or above to the above value. so i want to how we could calculate such scales. for an example main scale going with the inches and vernier scale also going with inches and devided in to some parts. so how could we calculate the measure .?????????

Good Explanation.

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Hi. Can you accurately measure the thickness of a fine wire using a vernier calliper?

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at firt

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what all can we measure with vernier calipers

thanks, but don’t given least count of inches series

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thanks…………

what is the logic behind:

L.C.=1 M.S.D.-1L.S.D

pls reply..

sorry it is L.C. = 1msd – 1vsd

wrong ruined my physics

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hey can yoy please tell me if the vernier scale reading has has errors or no? please reply fast….i have my assignment due on friday!!!

also how do i divide 5.14 cm ± 0.005cm by 2

What is the logic behind 1M.S.D-1V.S.D?? Why that?

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(5.14+.005)/2=5.145/2=2.5725 or (5.14-.005)/2=5.135/2=2.5675

sinthu

Pleas give me my questins answer (on the which principal vernier caliper worked) perhaps= rac and pinion im correct B-)

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To find the negative zero error should we substract the number of vernier divisions coincided from the no of vernier divisions and then multiply by the least count

to find negative eroer we have to adour obesrve reading and negative eror and obeserv reading=msd reading+vsd coincidingmultiply leasst count

and negative eror = least count multiply dividion coincind with msd when both jaws are touch

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could u please write the calculations too?We dont have any apparatus to do…….!

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Your point is good but how that LC is derived is the point of my wory.lwill find out the formula l wants had it.

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if the diameter observed by vernier calliper is b/w 2.3and2.4.at this stage 8th division coincides with main scale .find correct answer……………………………………………..can u plz give the answer