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
Find the powers p and q required for dimensional consistency.
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:
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
Carry out a dimensional analysis of T, L, and g.
Ignore the dimensions of 2◊ because it is a dimensionless quantity.
Compare the above dimensional equation on both sides.
p + q = 0 …… (2)
Solve the above two equations.
Therefore the value of the power q is .