Science Puzzle
Mass of the Pendulum
Three pendulums hang from the same bar. All three have strings exactly one metre long. One bob weighs 100 g, one weighs 500 g, and one weighs 2 kg.
If you release all three from the same angle at the same time, which one returns to the start position first?
The Answer
All three arrive back at exactly the same time. The period of a simple pendulum depends only on its length and the local gravitational acceleration, not on the mass of the bob.
The formula is T = 2π√(L/g). Mass appears nowhere. This is because gravity accelerates all masses equally: a heavier bob is pulled harder, but it also has more inertia to overcome, and the two effects cancel out perfectly.
Galileo is said to have discovered this by watching cathedral chandeliers swinging during a service and timing them with his pulse. He noticed that long chandeliers took longer than short ones, but that the same chandelier always took the same time regardless of how far it swung or what it weighed.
This mass-independence is the same principle behind Galileo's famous (possibly legendary) experiment dropping different masses from the Leaning Tower of Pisa.
The principle: Pendulum isochronism. The period of a simple pendulum depends only on its length and gravitational acceleration, not on the mass of the bob. Heavier objects are pulled harder but resist acceleration proportionally.