suppose a pendulum use to show the rotation of the earth has a period of approximately 16.9 seconds. What is the length using formula T=2pi sq root L/32

just solve for L in

2π√(L/32) = 16.9
√(L/32) = 16.9/2π = 2.69
L/32 = 7.23
L = 231.51

To find the length of the pendulum, we can rearrange the formula T = 2π√(L/32) and solve for L.

Given that T = 16.9 seconds, we can substitute this value into the formula:

16.9 = 2π√(L/32)

To isolate L, we need to square both sides of the equation:

(16.9)^2 = (2π)^2(L/32)

Evaluating the expression:

285.61 = 4π^2(L/32)

Now, we can multiply both sides by 32 and divide by 4π^2:

285.61 * 32 / 4π^2 = L

Calculating:

2284.88 / 4π^2 ≈ L

L ≈ 57.92

Therefore, the approximate length of the pendulum is 57.92 units.

To find the length of the pendulum, we can rearrange the given formula for the period of a pendulum:

T = 2π√(L/32)

where T is the period of the pendulum and L is the length of the pendulum.

Since we know that the period of the pendulum is approximately 16.9 seconds, we can substitute this value into the formula:

16.9 = 2π√(L/32)

Now, let's solve this equation step by step to find the length of the pendulum.

Step 1: Divide both sides of the equation by 2π:

16.9 / (2π) = √(L/32)

Step 2: Square both sides of the equation:

(16.9 / (2π))^2 = L/32

Step 3: Multiply both sides of the equation by 32:

32 * (16.9 / (2π))^2 = L

Step 4: Calculate the value on the left side of the equation:

L ≈ 34.2497

Therefore, the length of the pendulum is approximately 34.2497 units.