Page 26 - Electrostatics-11

© GC Shiba
It is always possible to express physical quantities in terms of dimension if it

holds unit?

➢ No, not all the physical quantities can be expressed in terms of dimension if

it holds unit. For e.g., angle, it has the unit of radian but not dimension. The

converse is always possible. (dimension is possible in only of basic units).

Application of dimensional analysis

i. To check the correctness of a physical equation.

With the help of dimensional analysis, we can check whether the given

equation is dimensionally correct or not. We use principle of homogeneity i.e.;

dimension of left-hand side is equal to the dimension of right-hand side.

A correct physical equation must have the same dimensions for both

sides.

2
For e.g.: Check the correctness of formula for escape velocity (V) = √

Here, Dimensional formula for L.H.S. = [ −1 ]

[ −1 3 −2 ][ ] −1
2 −2
Dimensional formula for R.H.S. = √ = √ = [ ]
[ ]
∴, Dimension of L.H.S.= Dimension of R.H.S.

Hence, the given equation is dimensionally correct .

ii. To establish a relation among physical quantity.
E.g.: The time period of a simple pendulum may depend on the length of the

string (L), mass of bob (M) and acceleration due to gravity (g).

So, ∝ , ∝ , ∝
Combining these relations, we get

∝

, = … … … ( )
Writing equation (i) in dimensional form

]
[ ] = [ ] [ ] [ −2

, [ ] = [ + −2 ]

3 Mechanics