Answer:
We can use the formula for the period of a pendulum:
T = (2 * pi * sqrt(L/g))
where:
T = period (in seconds)
pi = 3.14159...
L = length of the pendulum (in meters)
g = acceleration due to gravity (9.81 m/s^2)
We can solve for L by rearranging the formula:
L = (T^2 * g) / (4 * pi^2)
We are given that the pendulum swings 20 times in 25 seconds. The period of one swing is the time it takes to complete one full cycle, so the period of 20 swings is 25 seconds divided by 20 swings, or 1.25 seconds.
Using this value for T and plugging in g, we get:
L = (1.25^2 * 9.81) / (4 * 3.14159^2)
L ≈ 0.153 meters or 15.3 centimeters
Therefore, the length of the pendulum is approximately 15.3 centimeters.