# 2. 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

## 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

## 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.