First slide

Simple hormonic motion

Question

A hollow sphere is filled with water. It is hung by a long thread to make it a simple pendulum. As the water flows out of a hole at the bottom of the sphere, the frequency of oscillation will

Moderate

A

go on increasing
B

go on decreasing
C

first increases and then decreases
D

first decreases and then increases

Solution

Frequency of a simple pendulum $f = \frac{1}{2 π} \sqrt{\frac{g}{l}}$
Evidently, $f \propto \frac{1}{\sqrt{l}}$ 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 of the hole at the bottom, the CG descends 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 decrease, thereby increasing the frequency.

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