Example:
An expression for the time period T of a simple pendulum can be obtained by using this method as follows.
Let true period T depend upon
1. Mass m of the bob
2. Length l of the pendulum and
3. Acceleration due to gravity g at the place where the pendulum is suspended. Let the constant involved is k = 2π.
Here k is the dimensionless constant. Rewriting the above equation with dimensions.
Comparing the powers of M, L and T on both sides, a = 0, b + c = 0, -2c = 1
Solving for a, b and c ⇒ a = 0, b = 1/2, and c = -1/2
From the above equation
Experimentally k = 2π, hence
T = 2π \(\sqrt {l/g}\)