**Dimensional Analysis**

Any calculations involving the use of the dimensions of the different physical quantities involved is called **dimensional analysis.**

It is used for any one of the following purpose:

**(1) To convert a physical quantity in one type of units into some other units**:The method used is called factor label method or unit factor method.

**(a)** First determine the unit conversion factor

**(b)** Multiply the given physical quantity with the unit conversion factor, retaining the units of the physical quantity as well as that of the unit conversion factor in such a way that all units cancel out leaving behind only the required units.

For Example: Conversion of of pounds (lb) into kg.

1 kg =2.205 lb

**Question:** A man weigh 175 lb. Express his weight in kg.

**Answer:** 1 kg =2.205 lb

= 79.4 kg

**(2) In solving problems**

**Question :** What is the mass (in grams) of an aluminium block whose dimensions are 2.0 in. × 3.0 in. × 4.0 in. and whose density is 2.7 g/cm^{3} ? Given that 1 inch = 2.54 cm

**Answer : **Unit conversion factors are 1 = 2.54cm/1 inch = 1 inch/2.54 cm

Required mass (in g) = 2.0 in. x 3.0 in. x 4.0 in. x 2.54 cm/1 in. x 2.54 cm/1 in. x 2.54 cm/1 in. x 2.7/cm^{3}

= 1.1 × 10^{3 }g

Very helpful.