A hollow sphere filled with water is used as the bob of a pendulum Assume that the equation for simple pendulum is valid with the distance between the point of suspension and centre of mass of the bob acting as the effective length of the pendulum. If water slowly leaks out of the bob, how will the time period vary?

The initial condition is when the water is filled in the sphere, as shown in figure (A). When the water starts to drain out of the hollow sphere used as bob of the pendulum, the center of mass of the bob will shift below, as shown in figure (B). This will increase the length of the pendulum. Hence, time period will also increase. When the water is completely drained out of the sphere, then again center of mass will shift to center of the sphere, as shown in figure (C) and time period will again vary and comes back to its initial value.