Q. A hollow sphere is filled with water. It is hung by a long thread. As the water flows out of a hole at the bottom, the period of oscillation will:
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Solution:
Time period of simple pendulum $ T=2\pi \sqrt{\left( \frac{l}{g} \right)}\propto \sqrt{l} $ , where $ l $ is effective length. (i.e., distance between centre of suspension and centre of gravity of bob) Initially centre of gravity is at the centre of sphere [Fig. ]. When water leaks the centre of gravity goes down until it is half-filled [Fig. ]; then it begins to go up and finally it again goes at the centre [Fig. ]. That is effective length first increases and then decreases. As $ T\propto \sqrt{l} $ , so time period first increases and then decreases.
