1. Aim

To measure the diameter of a small spherical/cylindrical body and to measure the internal diameter and depth of a given beaker/calorimeter using Vernier Callipers, and hence calculate its volume.

2. Apparatus Used

• Vernier Callipers
• Spherical body (steel ball/marble)
• Cylindrical object
• Beaker/Calorimeter
• Cleaning cloth
• Calculator

3. Diagram

Fig.1: Vernier Callipers with labeled parts

4. Theory

A Vernier Callipers is a precision measuring instrument that can be used to measure internal and external dimensions with a high degree of accuracy. It consists of:

• Main Scale: It is graduated in millimeters or centimeters on which a Vernier scale slides.
• Vernier Scale: It is a small auxiliary scale that allows readings to be taken with greater precision than is possible with the main scale alone.
• External Jaws: Used to measure external dimensions like the diameter of a spherical or cylindrical object.
• Internal Jaws: Used to measure internal dimensions like the internal diameter of a beaker.
• Depth Probe: Used to measure depths of containers.

The principle of the Vernier scale is based on the fact that the Vernier scale is divided such that n divisions on the Vernier scale are equal to (n-1) divisions on the main scale. This allows for measurements with a precision of:

To find the volume of different objects:

• For a sphere: $V = \frac{4}{3} \pi r^3$, where r is the radius of the sphere.
• For a cylinder: $V = \pi r^2 h$, where r is the radius and h is the height of the cylinder.
• For a beaker/calorimeter (approximated as a cylinder): $V = \pi r^2 h$, where r is the internal radius and h is the depth of the beaker.

5. Formula

6. Procedure

1. Preliminary Steps:
   • Clean the Vernier Callipers and the objects to be measured.
   • Check that the Vernier Callipers is working properly by closing the jaws completely and verifying that the zero of the Vernier scale coincides with the zero of the main scale.
   • If there is a zero error, note it down and apply the correction to all measurements.
2. Measuring the Diameter of a Spherical Body:
   • Hold the sphere gently between the external jaws of the Vernier Callipers.
   • Close the jaws until they just touch the surface of the sphere without applying excessive pressure.
   • Note the reading on the main scale and Vernier scale.
   • Record the measurement in the observation table.
   • Repeat the measurement at different positions of the sphere and take the average value.
3. Measuring the Diameter of a Cylindrical Body:
   • Hold the cylinder between the external jaws of the Vernier Callipers.
   • Close the jaws until they just touch the curved surface of the cylinder.
   • Note the reading and record it in the observation table.
   • Repeat the measurement at different positions along the length of the cylinder.
   • Measure the length of the cylinder in a similar way and record it.
4. Measuring the Internal Diameter of a Beaker/Calorimeter:
   • Open the internal jaws of the Vernier Callipers and place them inside the beaker.
   • Expand the jaws until they touch the inner walls of the beaker.
   • Ensure the jaws are positioned to measure the diameter (through the center).
   • Note the reading and record it in the observation table.
   • Repeat the measurement at different positions and orientations.
5. Measuring the Depth of a Beaker/Calorimeter:
   • Place the beaker on a flat surface.
   • Use the depth probe of the Vernier Callipers to measure from the rim to the bottom of the beaker.
   • Ensure the depth probe is perpendicular to the rim.
   • Note the reading and record it in the observation table.
   • Repeat the measurement at different positions along the rim.
6. Calculate the Volumes:
   • Using the measured diameters and depths, calculate the volumes using the appropriate formulas.
   • Record all calculations clearly showing each step.

7. Observation Table

Zero Error Measurement

For Spherical Body

For Cylindrical Body

For Beaker/Calorimeter

8. Calculations

Least Count Calculation

Volume of the Spherical Body

Volume of the Cylindrical Body

Volume of the Beaker/Calorimeter

9. Result

1. The diameter of the given spherical body is ___ mm or ___ cm, and its volume is ___ cm³.
2. The diameter of the given cylindrical body is ___ mm or ___ cm, its length is ___ mm or ___ cm, and its volume is ___ cm³.
3. The internal diameter of the given beaker/calorimeter is ___ mm or ___ cm, its depth is ___ mm or ___ cm, and its volume is ___ cm³.

10. Precautions

1. Ensure the Vernier Callipers is clean and free from dust before use.
2. Check for zero error before taking any measurements and apply necessary corrections.
3. Always close the jaws of the Vernier Callipers gently to avoid excessive pressure on the object being measured.
4. When measuring internal diameter, ensure the internal jaws are positioned to measure through the center of the beaker.
5. Always read the Vernier scale from a position perpendicular to the scale to avoid parallax error.
6. When measuring the depth of a beaker, ensure the depth probe is perpendicular to the rim.
7. Take multiple readings at different positions and orientations to minimize random errors.
8. Handle the Vernier Callipers with care to avoid dropping or damaging it.
9. Lock the screw after taking a reading to ensure it doesn't change while recording.
10. Return the Vernier Callipers to its case after use to prevent damage.

11. Sources of Error

1. Zero Error: The Vernier Callipers may have a zero error if the zero of the Vernier scale does not coincide with the zero of the main scale when the jaws are completely closed.
2. Parallax Error: Reading the scales from an angle instead of perpendicular to them can lead to parallax error.
3. Temperature Effects: Metal expands when heated, which could affect both the Vernier Callipers and the object being measured.
4. Pressure Error: Applying excessive pressure while measuring can deform soft objects or the Vernier Callipers itself.
5. Calibration Error: Improper calibration of the Vernier Callipers can lead to systematic errors in all measurements.
6. Human Error: Misreading of scales, improper handling, or incorrect alignment of the jaws with the object.
7. Irregular Surfaces: Objects with irregular surfaces can lead to inconsistent measurements.
8. Wear and Tear: Worn out Vernier Callipers may not give accurate readings.
9. Measurement Technique: Improper placement of the Vernier Callipers, especially when measuring the internal diameter or depth.
10. Object Orientation: Not measuring the true diameter of spherical or cylindrical objects due to improper orientation.

12. Viva Voice Questions