Question

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:

• A. first increase and then decrease
• B. first decrease and then increase
• C. go on increasing
• D. go on decreasing

Answer 1

Answer: (A)

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.