question_answer

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

Correct Answer: A

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.