How does increasing the length of the pendulum affect its period?

How does increasing the length of the pendulum affect its period?

• A. Increases the period
• B. Decreases the period
• C. No effect on the period
• D. Halves the period

Answer: (A)

The correct understanding of how increasing the length of a pendulum affects its period is based on the principles of simple harmonic motion. The period of a simple pendulum, which is the time it takes to complete one full oscillation, is directly related to the length of the pendulum. As the length of the pendulum increases, the period also increases. This relationship is derived from the formula for the period of a simple pendulum, which states that the period \( T \) is proportional to the square root of the length \( L \) of the pendulum: \[ T = 2\pi \sqrt{\frac{L}{g}} \] Here, \( g \) is the acceleration due to gravity. From this equation, it can be observed that as \( L \) (the length of the pendulum) increases, \( T \) (the period) also increases. This indicates that a longer pendulum swings more slowly, and thus taking more time to complete each oscillation. When considering the other options, the decrease in period would imply that the pendulum swings faster with an increase in length, which contradicts the direct relationship established by the formula. Similarly, stating that there is no effect would ignore the

The correct understanding of how increasing the length of a pendulum affects its period is based on the principles of simple harmonic motion. The period of a simple pendulum, which is the time it takes to complete one full oscillation, is directly related to the length of the pendulum.

As the length of the pendulum increases, the period also increases. This relationship is derived from the formula for the period of a simple pendulum, which states that the period ( T ) is proportional to the square root of the length ( L ) of the pendulum:

[

T = 2\pi \sqrt{\frac{L}{g}}

]

Here, ( g ) is the acceleration due to gravity. From this equation, it can be observed that as ( L ) (the length of the pendulum) increases, ( T ) (the period) also increases. This indicates that a longer pendulum swings more slowly, and thus taking more time to complete each oscillation.

When considering the other options, the decrease in period would imply that the pendulum swings faster with an increase in length, which contradicts the direct relationship established by the formula. Similarly, stating that there is no effect would ignore the