Question

What are the uses/application and limitations of dimensional method

Answer 1

Dimensional Formula is useful for the following applications.

1.To check the correctness of the given equation. This use is based on the principle of homogeneity.

Principle of homogeneity:

It states only quantities of same dimensions can be added subtracted and equated. Hence in a Physical equation every term should have same dimensions.

2 . To convert one system of units into another system.

Eg: The numerical value of 10 joule in a new system of units in which the unit of mass is 10gm, unit of length 10cm. and unit of time 10sec. can be determined using the concept that

n₁u1 = n₂u₂

where n₁ ,n_{2 are the numerical values of a physical quantity and} u1,u_{2are the different units for same physical quantity.It means the original value of physical quantity remains same even when it is represented in different system of units.}
3 . To derive the equations showing the relation between different physical quantities.

Eg: When a spherical body falls through a viscous medium the upward viscous force acting on it depends upon

1. radius r of the body

2. coefficient of viscosity of the medium and

3. velocity v of the body.

LIMITATIONS OF DIMENSIONAL SYSTEM:

1 . Dimensionless quantities cannot be determined by this method. Constant of proportionality cannot be determined by this method. They can be found either by experiment (or) by theory.

2 . This method is not applicable to trigonometric, logarthmic and exponential functions.

3.In the case of physical quantities which are dependent upon more than three physical quantities, this method will be difficult.

4 . In some cases, the constant of proportionality also posseses dimensions. In such cases we cannot use this system.

5 . If one side of equation contains addition or subtraction of physical quantities, we can not use this method.