**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.**

**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:

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

…(1)

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)

And

… (3)

Solve the above two equations.

Therefore the value of the power q is .