A pendulum swings with a period of 2 seconds. What is the length of the pendulum?
Practice Questions
1 question
Q1
A pendulum swings with a period of 2 seconds. What is the length of the pendulum?
0.5 m
1 m
2 m
4 m
The period T of a simple pendulum is given by T = 2π√(L/g). Rearranging gives L = (T²g)/(4π²). Using g = 9.8 m/s², L = (2² * 9.8)/(4π²) ≈ 1 m.
Questions & Step-by-step Solutions
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Q
Q: A pendulum swings with a period of 2 seconds. What is the length of the pendulum?
Solution: The period T of a simple pendulum is given by T = 2π√(L/g). Rearranging gives L = (T²g)/(4π²). Using g = 9.8 m/s², L = (2² * 9.8)/(4π²) ≈ 1 m.
Steps: 11
Step 1: Understand that the period T of a pendulum is the time it takes to complete one full swing back and forth.
Step 2: Note that the period T is given as 2 seconds.
Step 3: Recall the formula for the period of a simple pendulum: T = 2π√(L/g), where L is the length of the pendulum and g is the acceleration due to gravity.
Step 4: Rearrange the formula to solve for L: L = (T²g)/(4π²).
Step 5: Substitute the values into the formula: T = 2 seconds and g = 9.8 m/s².
Step 6: Calculate T²: (2 seconds)² = 4 seconds².
Step 7: Substitute T² and g into the formula: L = (4 * 9.8)/(4π²).
Step 8: Simplify the equation: L = (39.2)/(4π²).
Step 9: Calculate the value of π (approximately 3.14) and then π² (approximately 9.86).
Step 10: Calculate 4π²: 4 * 9.86 = 39.44.
Step 11: Divide 39.2 by 39.44 to find L: L ≈ 1 meter.
