Officer Aptitude Rating (OAR) Test 2025 – 400 Free Practice Questions to Pass the Exam

Increasing the string length of a simple pendulum directly affects its swing time, also known as the period of the pendulum. The relationship between the period and the length of the string is described by the formula:

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

where \( T \) is the period (the time it takes to complete one full swing), \( L \) is the length of the string, and \( g \) represents the acceleration due to gravity.

From this formula, it is clear that the period \( T \) is proportional to the square root of the length \( L \). This means that if the string length increases, the period \( T \) also increases. Essentially, the longer the pendulum, the longer it takes to make a complete swing. This occurs because a longer string creates a greater arc for the pendulum to travel, which naturally lengthens the time taken to return to its starting position.

Therefore, the understanding of this relationship illustrates why increasing the string length leads to an increase in the swing time of a pendulum.