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(D) The time period of a simple pendulum is given by $T = 2 \pi \sqrt{L/g}$,where $L$ is the distance between the point of suspension and the center o

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first increase then decrease

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(D) The time period of a simple pendulum is given by $T = 2 \pi \sqrt{L/g}$,where $L$ is the distance between the point of suspension and the center of mass $(CM)$ of the system.Initially,the $CM$ of the water-filled sphere is at the geometric center of the sphere.As water flows out from the bottom hole,the $CM$ of the remaining water shifts downwards,which increases the effective length $L$ of the pendulum,causing the time period $T$ to increase.As the sphere becomes nearly empty,the $CM$ of the remaining water shifts back upwards towards the center of the sphere.This causes the effective length $L$ to decrease,which in turn causes the time period $T$ to decrease.Therefore,the period of oscillation first increases and then decreases.

$A$ hollow sphere is filled with water through a small hole in it. It is then hung by a long thread and made to oscillate. As the water slowly flows out of the hole at the bottom,the period of oscillation will

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