Measure the diameter of a Small Spherical Body Using Vernier Callipers

Introduction

Measuring diameter of a small spherical body using vernier calliper has many practical applications in our daily life. Measurements are fundamental to all scientific sections. It also plays a crucial role in our daily life. Seeing your height, buying milk for your house. Actions like timing your friend in a race require measurements. Measurement answers questions, like how long, how heavy, and how fast.

Measurement is the act of comparing an attribute or phenomenon of one object to the attribute or phenomenon of another object and assigning a numerical value to that object or phenomenon. Measurement is defined as determining the quantity and numerical value of an object. We use a meter scale to measure the lengths of objects in our daily life. They are marked in cm and mm.

What is a vernier calliper?

Generally, the dimensions of various objects can be calculated using a vernier calliper. After calculating the length, width, and height of objects, we can calculate their volume. For example, by calculating the inside diameter (using the correct jaws) and depth (using a depth gauge) of a nozzle, the internal volume of the nozzle can be calculated. Today we are living in the digital world.

Hence, the vernier scale also got a new evolution called the digital vernier scale. An indexing system and an electronic calculator are mounted on the slide of a digital vernier scale. It calculates the measurement and displays it with an indicator. Thus there is no need to calculate residual capacity, zero correction, etc. of the instrument used.

Least Count

The smallest value that a meter scale can measure is called its least count. A meter gauge has a resolution of 1mm. Using this we can calculate the length of the material to the nearest mm. We can measure to 0.1mm precision with a vernier calliper and 0.01mm precision with a screw gauge. Often the main scale division is marked in centimetres and its subdivisions in millimetres. So, the smallest size of the primary scale is one millimetre. A vernier scale has a total of 10 divisions.

$$\mathrm{Least count of the instrument =\frac{The\: value\: of\: the\: smallest\: division\: of\: the\: primary\: scale}{Total\: divisions\: of\: the\: vernier\: scale }}$$

$$\mathrm{L.C.=1mm/10=0.1 mm=0.01 cm.}$$

Aim

Calculate the diameter of a small sphere of known mass using a vernier caliper.

Material used

• Vernier calliper

• Solid sphere

Theory

The dimensions of various objects can be calculated using a vernier caliper. After calculating the length, width, and height of objects, we can calculate their volume. For example, by calculating the inside diameter (using the correct jaws) and depth (using a depth gauge) of a nozzle, the internal volume of the nozzle can be calculated.

Diagram

Fig.1. Vernier Calliper

A vernier calliper consists of a thin metal bar marked with cm and mm measurements. This is called the primary criterion. The left end of the metal bar has upward and downward jaws fixed perpendicular to the main scale. These are called fixed jaws. A slider with up and down moving jaws is mounted on the right side of the fixed jaw. Using a screw, the slider can be moved and fixed at a fixed position.

The measurements of the vernier scale are marked on the slider and it moves with the slider and the running jaw. Downward jaws are used to measure the external dimensions of an object and upward jaws are used to measure internal dimensions. A thin bar attached to the right-hand side of the vernier scale is used to measure the depth of non-input objects.

Procedure

• The zero error of the vernier calliper should be observed. Note observed errors.

• The sphere is fitted between the two poles of the vernier calliper and the primary scale reading (PSR) is noted.

• By noting which vernier scale division (VSD) exactly matches the Main scale reading, zero correction with this vernier scale division will give the correct vernier scale reading (VSR).

• This VSR is multiplied by the least count and added to the Main scale reading (MSR). This value is the diameter of the sphere.

• The diameter is observed for different positions of the sphere and its average diameter is found in the table. From this, the radius of the sphere is calculated.

Calculation

$$\mathrm{Vernier\: Scale\: Reading\: (VSR)=Vernier\: Scale\: Division\: (VSD)\:±\:Zero\: correction\:(Z.C)}$$

$$\mathrm{Diameter\: of\: the\: sphere\: D\:=\:MSR\:+\:(VSR \times LC) cm}$$

Result

The diameter of the given small spherical body by using a vernier calliper is ________ cm.

Source of Error

When measuring physical quantities, accuracy is essential. Accuracy refers to the degree to which the measurement we measure agrees with the true measurement. Inaccurate values are obtained due to faulty measuring instruments and errors of understanding by the measurer.

To obtain accurate measurements, it is always necessary to check the accuracy of the measuring instrument. Check that the zero division of the vernier scale matches the zero division of the primary scale. If they match, it means there is no swirl fault, if they don’t, it means there is a swirl fault in the meter. Zero error can be a positive error or a negative error. If the zero division is to the right of the main scale, it is called a positive zero error. Conversely, if it is to the left, it is called a negative zero error.

Conclusion

Measurements are fundamental to all scientific parts. It also plays a crucial role in our daily life. Measurement is defined as determining the quantity and numerical value of an object. The dimensions of various objects can be calculated using a vernier calliper. An indexing system and an electronic calculator are mounted on the slide of a digital vernier scale. It calculates the measurement and displays it with an indicator. A meter gauge has a resolution of 1mm. Using this we can calculate the length of the material to the nearest mm.

FAQs

1. What is Error?

The explanation for error may be the difference between the true value and the measured value. The actual value is the average value of multiple times the measured value.

2. What is Screw Gauge?

A screw gauge is a measuring instrument accurate to one-hundredth of a millimetre (0.01mm). This instrument can measure the diameter of thin wire, the thickness of thin metal plate, etc.

3.Define Gross error

Gross Errors are called human errors. The carelessness of an observer leads to gross error. For Example, when an observer takes the reading he may write 76 as 70. It is noted as an error.

4.How to reduce errors in measurement?

If the relative difference when calculated in percentage (%), is very large, it should be certainly rejected. Use the good condition instrument to reduce the error.

5.What is a random error?

The errors arising out of small changes in the experimental conditions and the personal judgment of the observer are known as random errors. When random errors are due entirely to chance, and not due to any personal bias on the part of the observer, they are likely to be positive as well as negatives.