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(D) The given system acts as a simple pendulum, where the effective length $(l)$ is the distance between the point of suspension and the center of gra

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First increase and then decrease to original value

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(D) The given system acts as a simple pendulum, where the effective length $(l)$ is the distance between the point of suspension and the center of gravity $(C.G.)$ of the oscillating body.Initially, when the sphere is full, the $C.G.$ is at the center of the sphere. As water flows out, the center of mass of the remaining water shifts downwards, causing the resultant $C.G.$ of the system to move downwards. This increases the effective length $(l)$, and since the time period $T = 2\pi \sqrt{l/g}$, the time period $T$ increases.As more water flows out, the weight of the remaining water becomes less than the weight of the empty sphere. The resultant $C.G.$ starts shifting back upwards towards the center of the sphere. Consequently, the effective length $(l)$ decreases, which causes the time period $T$ to decrease.Finally, when the sphere is completely empty, the $C.G.$ returns to the center of the sphere, making the effective length equal to its initial value. Thus, the time period returns to its original value. Therefore, the period of oscillation first increases and then decreases to its original value.

$A$ 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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