A simple pendulum has a hollow spherical bob which is completely filled with sand. It is set into small oscillations with an initial time period T₀ . A small hole at the bottom of the bob is opened, and the sand slowly leaks out until the bob is completely empty. Which of the following correctly describes the variation in the time period of the pendulum during this process?

Step-by-step solution

The time period of a simple pendulum is given by T = 2 L g , where L is the effective length from the point of suspension to the center of mass of the bob. Initially, the bob is completely filled, so the center of mass is at the geometric center of the sphere. As sand begins to leak, the center of mass of the remaining sand-bob system shifts downwards. This increases the effective length L , causing the time period T to increase. When the bob is more than half empty, the center of mass starts shifting back upwards.