Oscillations Ques 57
57. 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
Show Answer
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.
BETA
