Question

A grandfather clock has a pendulum that consists of a thin rod of length L and mass M, with a small mass m attached to the end. The pendulum swings back and forth with a period T. Which of the following factors will increase the period of the pendulum?

1) Increasing the length L of the rod
2) Increasing the mass M of the rod
3) Increasing the mass m attached to the end
4) Increasing the amplitude of the pendulum's swing

Answer 1

Increasing the length of the rod will increase the period of the pendulum. Increasing the mass of the rod, increasing the mass attached to the end, and increasing the amplitude of the pendulum's swing will not affect the period.

Step-by-step explanation:

The period of a pendulum is determined by its length and the acceleration due to gravity. Increasing the length of the rod (option 1) will increase the period of the pendulum. Increasing the mass of the rod (option 2) will not affect the period. Increasing the mass attached to the end (option 3) will also not affect the period. Lastly, increasing the amplitude of the pendulum's swing (option 4) will not affect the period as long as the amplitude is less than about 15°.