Measurement and Error

Dimensions

Dimensions are the power of fundamental quantities to be raised to express a physical quantity. The dimension of fundamental quantities are denoted as

Dimensional formula

The expression of a physical quantity in terms of Fundamental quantities involved with their proper dimension is called dimensional formula. For example the dimensional formula of velocity is [MoL1T−1].

Principle of homogeneity of dimensions

An equation is dimensionally correct if the dimensions of the various terms on either side of the equation are the same. This is called the principle of homogeneity of dimensions.

Dimensional Analysis and Its Applications

Dimensional formula based Problems

1. Unit conversion

2.To check the correctness of an equation

3. To establish relationship

4. Dimensions of a constant

Limitations of Dimensional Analysis

Precision, Accuracy, measurement and significant figures

Accuracy

Accuracy is a description of how close a measurement is to the correct or accepted value of the quantity measured.

Precision

Precision is the degree of exactness of a measurement.

Errors in Measurement

The uncertainty in the measurement of a physical quantity is called error. Errors may be classified into many categories.

1. Constant errors

2. Systematic errors

3. Gross error

4. Random errors