A pendulum swings with a period T. What is the period of a pendulum of length 4L
Practice Questions
Q1
A pendulum swings with a period T. What is the period of a pendulum of length 4L?
2T
T/2
T√2
2√2T
Questions & Step-by-Step Solutions
A pendulum swings with a period T. What is the period of a pendulum of length 4L?
Step 1: Understand that the period T of a pendulum is calculated using the formula T = 2π√(L/g), where L is the length of the pendulum and g is the acceleration due to gravity.
Step 2: Identify the new length of the pendulum, which is 4L (four times the original length).
Step 3: Substitute 4L into the formula for the period: T' = 2π√(4L/g).
Step 4: Simplify the equation: T' = 2π√(4) * √(L/g).
Step 5: Since √(4) equals 2, rewrite the equation as T' = 2 * 2π√(L/g).
Step 6: Notice that 2π√(L/g) is the original period T, so T' = 2 * T.
Step 7: Conclude that the period of the pendulum of length 4L is 2T.
Pendulum Period – The period of a simple pendulum is determined by its length and the acceleration due to gravity, following the formula T = 2π√(L/g).
Scaling of Length – Understanding how changes in the length of the pendulum affect the period, specifically that increasing the length increases the period.
