A pendulum swings back and forth with a period of 1 second. If the length of the pendulum is doubled, what will be the new period?
Practice Questions
1 question
Q1
A pendulum swings back and forth with a period of 1 second. If the length of the pendulum is doubled, what will be the new period?
1 s
1.41 s
2 s
4 s
The period of a simple pendulum is given by T = 2π√(L/g). If L is doubled, T becomes T' = 2π√(2L/g) = √2 * T ≈ 1.41 s.
Questions & Step-by-step Solutions
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Q
Q: A pendulum swings back and forth with a period of 1 second. If the length of the pendulum is doubled, what will be the new period?
Solution: The period of a simple pendulum is given by T = 2π√(L/g). If L is doubled, T becomes T' = 2π√(2L/g) = √2 * T ≈ 1.41 s.
Steps: 8
Step 1: Understand that the period of a pendulum (T) is the time it takes to swing back and forth once.
Step 2: Know that the formula for the period of a pendulum is T = 2π√(L/g), where L is the length of the pendulum and g is the acceleration due to gravity.
Step 3: The original period (T) is given as 1 second, and the original length (L) is some value.
Step 4: If the length of the pendulum is doubled, the new length becomes 2L.
Step 5: Substitute the new length into the formula: T' = 2π√(2L/g).
Step 6: Simplify the new period: T' = 2π√(2) * √(L/g).
Step 7: Notice that √(L/g) is the original period (T), so T' = √2 * T.
Step 8: Since T is 1 second, calculate T' = √2 * 1 second ≈ 1.41 seconds.
