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

Options

A. go on increasing
B. go on decreasing
C. first increases and then decreases
D. first decreases and then increases

Answer

D

Explanation

Frequency of a simple pendulum `f=(1)/(2pi)sqrt((g)/(l))`
Evidently, `fprop(1)/(sqrtl)` at any place.
The effective Length `l` is the distance of the point of suspension `O'` from the centre of gravity `(CG)` of the bob. As, water flows out from centre towards the bottom, increasing the effective length, and consequently `f` decreases.
However, when all the water has flows out the CG of a hollow sphere is once again at its centre and hence the effective length would decreases, thereby increasing the frequency.