The period T of a simple pendulum is the amount of time required for it to undergo one complete oscillation

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The period T of a simple pendulum is the amount of time required for it to undergo one complete oscillation, if the length of the pendulum is L and the acceleration of gravity is g, then T is given by image
Find the powers p and q required for dimensional consistency.

Answer:

Time period of a simple pendulum can be defined as the amount of time required to complete one oscillation.
Equation for the time period of a simple pendulum can be expressed as follows:
image
Here, L is the length of the pendulum, and g is the acceleration due to gravity.

Calculate the powers p and q.
The equation is
image …(1)
Carry out a dimensional analysis of T, L, and g.
Ignore the dimensions of 2◊ because it is a dimensionless quantity.
image
Compare the above dimensional equation on both sides.
p + q = 0 …… (2)
And
image … (3)
Solve the above two equations.
image
Therefore the value of the power q is image.