Oscillations - Result Question 55

60. 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 [1997]

(a) first increase and then decrease

(b) first decrease and then increase

(c) go on increasing

(d) go on decreasing

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Solution:

(a) Time period of simple pendulum

$T=2 \pi \sqrt{(\frac{l}{g})} \propto \sqrt{l}$ 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. When water leaks the centre of gravity goes down until it is half filled; then it begins to go up and finally it again goes at the centre. That is effective length first increases and then decreases. As $T \propto \sqrt{l}$, so time period first increases and then decreases.