The four pendulums shown have been cut from the same uniform sheet of board. They are attached to the ceiling with strings of equal length. Which pendulum has the shortest period?
Answer
Physics Behind the Shortest Period Pendulum
When multiple pendulums are made from the same uniform material and suspended using strings of equal length, their periods of oscillation depend not only on the string length but also on their shape and mass distribution.
Understanding the Center of Mass
Each pendulum, although made of the same material, has a different shape. This causes the center of mass of each pendulum to be located at a different point. The closer the center of mass is to the pivot, the shorter the effective length, and hence, the shorter the time it takes to complete one oscillation.
Time Period of a Physical Pendulum
Where:
- Leff is the distance between the pivot and the center of mass
- g is the acceleration due to gravity
This formula shows that a shorter effective length results in a shorter period of oscillation.
Which Pendulum Has the Shortest Period?
According to the visual indicators of the center of mass in the pendulums, Pendulum D has its center of mass located closest to the point of suspension. This means it has the shortest effective length among the four, and therefore, the shortest period.
Conclusion
Pendulum D oscillates the fastest because its center of mass is higher up, reducing the distance the mass swings and decreasing the time it takes to complete one full oscillation.