## Vernier Caliper Experiment

**Vernier Caliper Experiment for Class 11 ****with Readings**

**EXPERIMENT - 1, ****VERNIER CALIPERS - I**

**Aim:**

i. To find the volume of the sphere by measuring its diameter.

ii. To determine the internal diameter, depth and volume of a calorimeter.

**Apparatus:**

Vernier calipers, Calorimeter, Given sphere etc. The vernier calipers consist of a main scale and a sub scale called vernier scale. The main scale is graduated in cm with a fixed jaw A at one end. A movable jaw B, provided with a vernier scale, slides over the main scale. This can be fixed at any point. When the jaws are in contact, the zero of the vernier coincides with the zero of the main scale. The jaws are provided with extensions C and D which are used in the measurement of inner diameter.

**Principle **

i. Least count of the Vernier = Mamitude of one main scale division / No. of divisions on the vernier scale

ii. Total reading = M.S.R. + (V.S.R. x LC.)

where,

M.S.R. = Main Scale Reading

V.S.R. = Vernier Scale Reading

L.C. = Least Count

iii. Volume of the sphere V= 4/3 πr^{3} where, r = Radius
of the sphere

iv. Volume of the calorimeter V= πR^{2}h

where, R = Internal radius of the calorimeter

h = Depth of the calorimeter

**Procedure **

The least count of the vernier calipers is determined by noting the magnitude of one main scale division and number of divisions on the vernier scale.

L.C. = 1 msd / n

**i. To find the volume of the sphere**

To measure the diameter of the sphere, it is gripped between the jaws A and B. The main scale reading (M.S.R), just before the zero of the vernier and the vernier scale reading (V.S.R.), coinciding with any of the main scale reading are noted. Diameter of the sphere = M.S.R. + ( V.S R. x LC). This procedure is repeated by changing the position of the sphere and the mean diameter (d) of the sphere is determined. Hence the volume of the sphere can be calculated.

**ii. To find the volume of the calorimeter **

To find the volume of the calorimeter, the vertical projections of the jaws C and D are put inside the calorimeter. Open the jams till they are held tight between the walls of the calorimeter. The M.S.R. and V.S.R. are noted as mentioned above and the inner diameter is determined. The strip (T) attached on the backside of the vernier is pushed out. Keep the right edge of the main scale strip on the upper edge of the calorimeter. Make the tip of the strip touching the bottom of the calorimeter. The M.S.R. and V.S.R. we noted as mentioned above and the depth is determined. Hence the volume of the calorimeter can be calculated.

The calorimeter is filled with water. This water is poured into a graduated measuring jar and the volume is measured. This volume is compared with calculated volume.

**Observations and Readings:**

Magnitude of one main scale division, 1 msd = __0.1 cm__

Number of divisions on the vernier, n = __10__

Least count (L.C.) = 1 msd/n = __0.04 cm__

**i. To find the volume of the sphere**

Radius of the sphere, r = d/2 = __0.985__ cm

Therefore, Volume of the sphere = V= 4/3 πr^{3} = __4 x 10__^{-6} m^{3}

**ii. To find the volume of the calorimeter**

__2.48 cm__=

__2.48 x 10__

^{-2 }m

Depth of the calorimeter, h = __7.54 cm__ = __7.54 x 10__^{-2 }m

Internal volume of the calorimeter = πR^{2}h = __1.45 x 10__^{-4 }m^{3}

**Results **

i. Volume of the sphere = __4 x 10__^{-6} m^{3}

ii. Internal volume of the calorimeter

a. with vernier calipers = __1.45 x 10__^{-4} m^{3}

**EXPERIMENT - 2, VERNIER CALIPERS - II**

**Aim:**

i. To find the volume of the cylinder by measuring its length and diameter.

ii. To determine the volume of the given rectangular block by measuring its dimensions and verify the result using a measuring jar

**Apparatus:**

Vernier calipers, The given cylinder, Metallic block, Measuring jar, Water etc.

The vernier calipers consists of a main ale and a sub scale called vernier scale. The main scale is graduated in mm. with a fixed jaw A in one end. A movable jaw B, provided with a vernier scale, slides over the main scale. This can be fixed at any point. When the jaws are in contact, the zero of the vernier coincides with the zero of the main scale. The jaws are provided with extensions C and D which are used in the measurement of inner diameter.

**Principle: **

i. Least count = Magnitude of one main scale division/No. of divisions on the vernier scale

ii. Total reading = M.S.R + (V.S.R. x L.C.)

where,

M.S.R = Main Scale Reading

V.S.R = Vernier Scale Reading

L.C = Least Count

iii. Volume of the cylinder, V = πr^{2}L

where, r = Radius of the cylinder

L = Length of the cylinder

iv. Volume of the rectangular block V = l.b.t

where,

l = Length of the rectangular block

b = Breath of the rectangular block

t = Thickness of the rectangular block

**Procedure:**

The least count of the vernier calipers is determined by noting the magnitude of one main scale division and number of divisions on the vernier scale,

L.C = 1 msd/n

**i. To find the volume of the cylinder:**

To measure the length of the cylinder, it is gripped lengthwise between the jaws A and B. The main scale reading (M.S.R.), just before the zero of the vernier and the vernier scale reading (V.S.R) coinciding with any of the main scale reading are noted. The length of the cylinder = M.S.R. + (V.S.R. x LC.). This procedure is repeated by changing the position of the cylinder. In the similar way the diameter of the cylinder is determined. Half of the diameter gives the radius (r). The volume of the cylinder can be found using the formula given ab6ve.

**ii. To find the volume of the rectangular block **

The length (l), breadth (b) and thickness (t) of the rectangular block are determined as in the above measurement.

Using a measuring jar, volume of the rectangular block can be
found. The given measuring jar is half filled with water. The reading of water
level is taken as V. The block whose volume is to be determined is gently
immersed into the water in the jar. The new water level is taken as V_{2}.
Then the volume of the block = V_{2} —V_{1}

**Observations and Readings**

Magnitude of one main scale division, 1 msd = __0.1 cm__

Number of divisions on the vernier, n = __10__

Least count (L.C.) = 1 msd/n = __0.01 cm__

**i. To find the volume of the cylinder**

Diameter of the cylinder, d = __1.015 cm__

Radius of the cylinder, r = d/2 = __0.5075 cm__

Length of the cylinder, L = __3.85 cm__

Therefore Volume of the cylinder = πr^{2}L = __3.11 x
10__^{-6 }m^{3}

**ii. To find the volume of the rectangular block**

Length of the rectangular block, (l) = __1.85 cm__

Breadth of the rectangular block, (b) = __1.85 cm__

Thickness of the rectangular block, (t) = __1.85 cm__

Therefore, Volume of the rectangular block, (v) = lbt =__ 6.33 x 10__^{-6 }m^{3}

Mass of the given block, M = ………..kg

Density, D = M/V = ………kgm^{-3}

**Measuring jar readings:**

Initial water level reading on the measuring jar, V_{1} = __41 cc__

Final water level reading on the measuring jar, V_{2} = __48 cc__

Therefore Volume of the block = V_{2} – V_{1} = __7 cc__ = __7 x 10__^{-6} m^{3}

**Results **

i. Volume of the cylinder = __3.11 x 10__^{-6 }m^{3}

ii. Volume of the rectangular block

a. with vernier calipers = __6.33 x 10__^{-6 } m^{3}

b. with measuring jar = __7 x 10__^{-6 }m^{3}

iii. Density of the rectangular block = ……….. kgm^{-3}

**MODEL VIVA VOCE QUESTIONS AND ANSWERS **

*1. What is vernier? Why is it so named? *

Vernier is a device for measuring small lengths accurately, correct upto a fraction of a millimetre. It is so named as it was devised by a French Mathematician, Paul Vernier.

*2. State three uses of a vernier calipers. *

(i) To measure length of small object

(ii) To measure internal diameter of beaker.

(iii) To determine surface area and volume of sphere.

*3. Name the instrument you could use for the measurement of
internal and external diameter of a beaker. *

Vernier calipers.

*4. What is meant by least count of a measuring instrument? *

The smallest value of physical quantity which can he measured accurately by the instrument.

*5. What is a vernier constant? *

It is the difference between a main scale division and a vernier scale division.

*6. What is meant by zero error of vernier calipers? *

On bringing the jaws of vernier calipers in contact with each other, some times the zero of the vernier scale may not coincide with the zero of the main scale. Thus the vernier calipers is said to possess zero error.

*7. How does zero error creep in this instrument? *

It is due to (i) wear and tear on account of the long use of the instrument, (ii) manufacturing defect.

*8. What is the function of the upper jaws of the vernier
calipers? *

The function of the upper jaws of the vernier calipers is to measure the internal dimensions of hollow objects.

## PN Junction Thermometer

**Investigatory
Project on PN Junction Thermometer**

**Aim:** To construct a thermometer using
semiconductor diode, calibrate it and to measure the unknown temperature of a
bath.

**Materials
and Apparatus**

(i) A
germanium diode (OA 79, DR 25 or DS 10)

(ii) High resistance
rheostat

(iii) 0 –
100 microammeter

(iv) Dry
cell (9V)

(v) Oil
bath (a tumbler and oil)

(vi)
Thermometer etc.

**Principle**

I_{s} = CT^{3}e^{-(Eg/kT)}

Where E_{g}
is the forbidden energy, T the temperature of the diode, K Boltzman’s constant
and C is a constant.

Taking
logarithm,

log_{e }I_{s}
= log_{e} (CT^{3}) – (E_{g}/k) x (1/T)

In the
operating range of the diodes, the temperature dependence of I_{s }is
mainly determined by the second term of the above equation. Hence, a plot of
log_{e }I_{s} against (1/T) is approximately linear. The slope
of the graph gives – (E_{g}/k).

**Procedure**

The circuit
is wired as shown in the figure. The diode is fixed to the cap of tumbler. Two
holes are provided on the cap and a thermometer is inserted in one and a wire
stirrer in the other. The tumbler is filled with oil heated to about 150°C. The cap is fixed and the oil is stirred well. At any particular
temperature T, the current is measures as a function of the reverse bias
voltage V. The reverse voltage is measured with a digital multimeter. The
reverse current is measured by the microammeter. From this reverse saturation
current I_{s} i.e., the steady reverse current, is noted. The cap of
the tumbler is opened and the temperature of the oil is allowed to fall by,
say, 20°C. The cap is fixed and the reverse saturated current is determined as
before. The temperature T and the saturated current I_{s}, are property
tabulated.

A graph is
drawn with log_{e }I_{s} and (1/T). The graph is a straight
line. It is the calibration curve of the diode thermometer. To find the unknown
temperature of a bath the saturation current I_{s} is measure keeping
the diode in the bath. From the calibration curve, the temperature of the bath
can be found.