A simple pendulum consists of a bob, which is a hollow sphere filled with a liquid completely. If a hole is made into the sphere at its bottom so that the liquid starts flowing out of it, how will the time period of the pendulum be affected? Consider that the liquid has uniform density.

Explanation

When the sphere is initially filled with the liquid completely, its centre of gravity lies at its centre. When the liquid begin to drain, the centre of gravity begins to shift below the centre of the sphere. As a result, effective length of the pendulum increases and hence, its time period increases.
Now, when the sphere is more than half emptied, its centre of gravity begins to rise up. As a result, the effective length of the pendulum decreases and its time period decreases. At the instant when the entire liquid is drained out, the centre of gravity once again gets shifted to the centre of the sphere, the time period will attain its initial value.