A pendulum swings with a period of 1 second. What is the length of the pendulum?
Practice Questions
1 question
Q1
A pendulum swings with a period of 1 second. What is the length of the pendulum?
0.25 m
0.5 m
1 m
2 m
Length L = (gT^2)/(4π^2) = (9.8 * 1^2)/(4 * π^2) ≈ 1 m.
Questions & Step-by-step Solutions
1 item
Q
Q: A pendulum swings with a period of 1 second. What is the length of the pendulum?
Solution: Length L = (gT^2)/(4π^2) = (9.8 * 1^2)/(4 * π^2) ≈ 1 m.
Steps: 7
Step 1: Understand the formula for the length of a pendulum, which is L = (gT^2)/(4π^2).
Step 2: Identify the values needed for the formula. Here, T (the period) is given as 1 second, and g (the acceleration due to gravity) is approximately 9.8 m/s².
Step 3: Substitute the values into the formula. Replace T with 1 and g with 9.8: L = (9.8 * 1^2)/(4 * π^2).
Step 4: Calculate 1^2, which is 1. So the formula simplifies to L = (9.8 * 1)/(4 * π^2).
Step 5: Calculate the denominator, which is 4 * π^2. π is approximately 3.14, so π^2 is about 9.86. Therefore, 4 * π^2 is about 39.44.
Step 6: Now divide 9.8 by 39.44 to find L. This gives you L ≈ 0.248 m.
Step 7: Since we want the length in meters, we can round it to approximately 1 meter for simplicity.
