The bob of a simple pendulum is hollow and has been filled with w… - Vidyadip

Question

The bob of a simple pendulum is hollow and has been filled with water. There is a small hole below it. If this sphere continuously performs simple harmonic motion and water keeps falling out of the hole, then how will the period of oscillations change?

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Answer

When the sphere is completely filled with water, its center of mass is located at the center of sphere, let its period be T. As the water moves towards the sphere, its center of mass moves down. Due to this the length increases, therefore, initially the value of period increase. When all water comes out, the center of mass comes back to the center and due to this the value of period again becomes equal to previous value.

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