Question

Define dimensional formula. Give uses of dimensional analysis. Write down the limitations.

Answer 1

Dimension formula tells about which fundamental quantities are there in the physical quantity given.

It is represented in square brackets. For example length is denoted as $\left[L\right]$

If we know the physical quantities on which are used in the formula, dimensional analysis can be used to calculate the how the powers of these quantities will vary. For example if we know that the velocity depends upon length and time we can calculate the powers of the base quantities.

$\left[L^1{M}^0{T}^{-1}\right]=\left[L^a{M}^b{T}^c\right]$ now $a,b,c$ can be calculated.

The very limitation of the dimensional analysis is if the given formula carries the sum of two quantities and if only one of those quantities is provided dimensional analysis can’t be used to verify if the formula is correct or not.

$s=ut$

$s=\frac{1}{2}a{t}^2$

Both are dimensionally correct but the formula is not correct form of equation of motion.