A pendulum swings with a period T. What is the period of a pendulum of length 4L

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Question: A pendulum swings with a period T. What is the period of a pendulum of length 4L?

Options:

Correct Answer: 2T

Solution:

The period T of a simple pendulum is given by T = 2π√(L/g). For length 4L, T\' = 2π√(4L/g) = 2T.

A pendulum swings with a period T. What is the period of a pendulum of length 4L?

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.