The period P of a simple pendulum is the time for one complete swing. How does P depend on the mass m of the bob, the length l of the string, and the acceleration due to gravity g?

Explanation

To determine how the period \( P \) of a simple pendulum depends on the mass \( m \) of the bob, the length \( l \) of the string, and the acceleration due to gravity \( g \), we can use dimensional analysis. Here’s a step-by-step solution:

### Step 1: Identify the variables
The variables involved are:
- \( P \): the period of the pendulum (time)
- \( m \): the mass of the bob (mass)
- \( l \): the length of the string (length)
- \( g \): the acceleration due to gravity (length/time²)
...