To Use A Vernier Caliper To Measure Length External And Internal Diameter Of A Tube And Hence Find Volume And Density Of The Material Of The Tube

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APPARATUS REQUIRED:

1. Vernier caliper

2. A hollow tube

3. Any balance for  measuring mass

THEORY:

Principle of vernier

Vernier caliper consists of two scales and the vernier scale. These scales

are graduated in such a way that divisions of vernier scale coincide with (n-1) divisions of main scale in the principle of vernier caliper.

Then,

n usd consists with (n-1) msd.

1 usd consists with (n-11 / n ) msd.

Therefore, vernier constant (VC) = (1 msd – 1 usd) x value of 1 msd

      ={1 -(n-1) / n } x value of msd

      = I / n  x values of 1 msd

= value of 1 main scale division / total no. of division on vernier scale

Volume and density of hollow tube:-

Let l is the length, di is the internal and de is the external diameter of the tube. Then,

External volume of the tube, ve= πd²el / 4

       ve = πd²el / 4

Internal volume of the tube, vi=πd² / 4 i

Hence, volume of the tube, v= π(d²/e -d²/i)2 / 4

        = πl(de + di ) (de – di ) / 4

Density (D) of the material of the given tube is defined as mass (M) of the tube pen unit volume of the material of the tube.

i.e P= M / V

OBSERVATIONS:

1. For vernier constant

In the main scale, value of 10 main scale division = 1 cm

value of 1 main scale division = 0.1

In the vernier scale,

Total no. of vernier scale division (n)=10

therefore, V.S.= 1/ n  x value of 1 msd = OVL

Observation forNo.of Obs.Main scale reading (v)Vernier scale readingValue of vernier scale readingTotal z=(x+y)cmMain value z cmConnected mean value z +error cm 
length1.5.270.095.175.35.3±0=5.38
2.5.180.075.48
3.5.190.075.29
4.5.390.095.19
5.5.170.075.37
External diameter1.2.440.042.442.442.54±0=2.54
2.2.430.032.43
3.2.440.042.44
4.2.450.052.45
5.2.450.052.45
Internal diameter (di)1.2.180.082.182.1742.174±0=2.174
2.2.170.072.17
3.2.190.092.19
4.2.160.062.16
5.2.170.072.17

CALCULATIONS:

FROM TABLE:

l = 5.3

de = 2.44

di = 2.174

Volume of the table, V= πl (de+di) (de-di) / 4

                                = π 5.3 (2.44 +2.174) (2.44-2.175) / 4

      = 5.186cm³

Mass of the hollow tube = 8.65gm

Density of the material of the tube : P = m/v  = 8.65/3.64 = 2.376

PERCENTAGE ERROR:

Standard value density of maternal of the tube, PS = 2.7gm/cm³

Observed value of density of maternal of the tube PO = 2.376gm km³

Percentage error = |Ps – Po /Ps| x 100%

        = |2.7 – 2.376 / 2.7| x 100%

= 12%

RESULT:

The volume and density of material of the given tube are found to be 3.64 cm³ and 2.37cm ³ and 2.37 gm/cm ³ experimentally

CONCLUSIONS:

The length, internal and external diameters of a given hollow tube are measured by using vernier calipers and hence volume and density the material of the tube is determined.

SOURCES OF ERRORS:

1. Undve pressure applied to the jaus. 

2.  Non-uniformity in shape of the block.

3. Porallox may be three in taking observations.

PRECAUTIONS:

1. The zero error should be determined and applied carefully.

2. Two jaus should be pressed gently.

3. Observations should be taken at different points of the table.

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