A pendulum swings with a period of 1 second. If the length of the pendulum is tripled, what will be the new period?
Practice Questions
1 question
Q1
A pendulum swings with a period of 1 second. If the length of the pendulum is tripled, what will be the new period?
1 s
2 s
3 s
√3 s
The period T = 2π√(L/g). If L is tripled, T becomes √3 times longer, so T = 2 s.
Questions & Step-by-step Solutions
1 item
Q
Q: A pendulum swings with a period of 1 second. If the length of the pendulum is tripled, what will be the new period?
Solution: The period T = 2π√(L/g). If L is tripled, T becomes √3 times longer, so T = 2 s.
Steps: 8
Step 1: Understand that the period of a pendulum (T) is related to its length (L) using the formula T = 2π√(L/g), where g is the acceleration due to gravity.
Step 2: Note that the original period of the pendulum is 1 second, which means T = 1 s when L is the original length.
Step 3: If the length of the pendulum is tripled, we can express the new length as L' = 3L.
Step 4: Substitute L' into the period formula: T' = 2π√(3L/g).
Step 5: Factor out the original period: T' = 2π√3 * √(L/g) = √3 * T.
Step 6: Since the original period T is 1 second, we calculate the new period: T' = √3 * 1 s.
Step 7: Approximate √3, which is about 1.732, so T' is approximately 1.732 seconds.
Step 8: Round the result to the nearest whole number if needed, but the exact new period is 1.732 seconds.
