# 5. The length of a simple pendulum with a period on Earth of one second is most nearly

a.) 0.12 m
b.) 0.25 m
c.) 0.50 m
d.) 1.0 m
e.) 10.0 m

The formula for the period is
P = 2 pi sqrt(L/g)
g is the acceleration of gravity, 9.8 m/s^2.
Solve for L. (or get out a piece of string and do the experiment.)

## Pendulum period in seconds

T ≈ 2π√(L/g)
L is length of pendulum in meters
g is gravitational acceleration = 9.8 m/s²
Length for 1 second = 0.248 m
(b)

## Well, if you're willing to go through all that trouble with a piece of string, I applaud your dedication! But let me save you some time.

We have the equation P = 2π√(L/g), where P is the period and g is the acceleration due to gravity.

Let's solve for L:
L = (P/(2π))² * g

Substituting the given values:
L = (1/(2π))² * 9.8

Calculating that out:
L ≈ 0.123 m

So, the length of the pendulum with a period of one second on Earth is most nearly 0.12 m.
That one was closer than a trip to the amusement park!

## To find the length of the simple pendulum, we can rearrange the formula for the period:

P = 2π√(L/g)

Solving for L, we have:

L = (P/2π)^2 * g

Substituting the values given, with P = 1 second and g = 9.8 m/s^2, we can calculate:

L = (1 / (2π))^2 * 9.8

L = (1 / (2 * 3.14159))^2 * 9.8

L ≈ (0.159155)^2 * 9.8

L ≈ 0.025179 * 9.8

L ≈ 0.247

Therefore, the length of the simple pendulum with a period of one second is most nearly 0.25 m, which is option b).

## To find the length (L) of the simple pendulum with a period of one second on Earth, we can use the formula:

P = 2π√(L/g)

where P is the period, L is the length of the pendulum, and g is the acceleration due to gravity (approximately 9.8 m/s² on Earth).

So, we need to rearrange the formula to solve for L:

P = 2π√(L/g)
P² = 4π²(L/g)
L/g = P² / (4π²)
L = (P² / (4π²)) * g

Now, we can substitute P = 1 second and g = 9.8 m/s² into the equation to find the length L:

L = (1² / (4π²)) * 9.8
L = (1 / (4π²)) * 9.8
L = 0.246 m

So, the length of the simple pendulum with a period of one second on Earth is approximately 0.25 m.

Therefore, the answer is option b) 0.25 m.