IIT JEE Blogs

To find the unit of a given physical quantity in a given system of units:

ü      By expressing a physical quantity in terms of basic quantities we find its dimensions. In the dimensional formula replacing M, L, T by the fundamental units of the required system, we get the unit of physical quantity. However, sometimes we assign a specific name to this unit.

Example

Force is numerically equal to the product of mass and acceleration

i.e. Force = mass × acceleration

Its unit in SI system will be Kgms^-2 which is given a specific name “Newton (N)”.

Similarly, its unit in CGS system will be gm cms^-2 which is called “dyne”.

To find dimensions of physical constants or coefficients

The dimensions of a physical quantity is unique because it is the nature of the physical quantity and the nature does not change. If we write any formula or equation incorporating the given physical constant, we can find the dimensions of the required constant or co-efficient.

Example

From Newton’s law of Gravitation, the force exerted by one mass upon another is

To convert a physical quantity from one system of units to another

This is based on the fact that for a given physical quantity,

magnitude × unit = constant

So, when unit changes, magnitude will also change.

Example

1.         Convert one Newton into dyne

Sol. Dimensional formula for Newton  = [ML/T²]

or 1 N = 1 Kg m/s²    But 1 kg = 10³g

and 1 m = 10²cm

1N = (10³ g) ( 10²cm)/s² = 10^5 g cm/s² = 10^5 dyne

To check the dimensional correctness of a given physical relation

This is based on the principle that the dimensions of the terms on both sides of an equation must be same. This is known as the ‘principle of homogeneity’. If the dimensions of the terms on both sides are same, the equation is dimensionally correct, otherwise not. It is not necessary that a dimensionally correct equation is also physically correct but a physically correct equation has to be dimensionally correct.

Þ        Consider the formula, T = 2Π √(1/g)

where T is the time period of oscillation of a simple pendulum in a simple harmonic motion, l and g are the length of the pendulum and gravitational constants respectively. Check this formula, whether it is correct or not, using the concept of dimension.

Thus the above equation is dimensionally correct (homogeneous) and later you will come to know that it is physically also correct.

Þ        Consider the formula

Check this formula, whether it is correct or not, using the concept of dimension.

Dimensionally

In this case also the formula is dimensionally correct but, you know that it is physically incorrect as the correct formula is given by