A pendulum swings with a period of 1 second. If the length of the pendulum is in
Practice Questions
Q1
A pendulum swings with a period of 1 second. If the length of the pendulum is increased to four times its original length, what will be the new period?
1 s
2 s
4 s
√4 s
Questions & Step-by-Step Solutions
A pendulum swings with a period of 1 second. If the length of the pendulum is increased to four times its original length, what will be the new period?
Step 1: Understand that the period of a pendulum (T) is the time it takes to complete one full swing.
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 of the pendulum is given as 1 second. This means T = 1 second when L is the original length.
Step 4: If the length of the pendulum is increased to four times its original length, we can write this as L = 4L (where L is the original length).
Step 5: Substitute 4L into the period formula: T = 2π√(4L/g).
Step 6: Simplify the equation: T = 2π√(4) * √(L/g). Since √(4) = 2, we have T = 2 * 2π√(L/g).
Step 7: Notice that 2π√(L/g) is the original period (1 second), so we can replace it: T = 2 * 1 second.
Step 8: Therefore, the new period T is 2 seconds.
Pendulum Period Formula – The period of a pendulum is determined by its length and the acceleration due to gravity, expressed as T = 2π√(L/g).
Effect of Length on Period – Increasing the length of the pendulum affects the period, specifically, if the length is quadrupled, the period increases by a factor of √4.
