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(B) The time period $T$ of a simple pendulum is given by the formula $T = 2\pi \sqrt{\frac{l_{eff}}{g}}$,where $l_{eff}$ is the effective length of th

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$T$ increases first and then decreases

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(B) The time period $T$ of a simple pendulum is given by the formula $T = 2\pi \sqrt{\frac{l_{eff}}{g}}$,where $l_{eff}$ is the effective length of the pendulum.$l_{eff}$ is the distance between the point of suspension and the center of mass of the bob.Initially,when the bob is full of water,the center of mass is at the geometric center of the bob.As water flows out,the center of mass of the system (bob + remaining water) shifts downwards,which increases the effective length $l_{eff}$. Consequently,the time period $T$ increases.As the water level continues to drop and the bob becomes empty,the center of mass eventually rises back to the geometric center of the bob.Since the effective length $l_{eff}$ decreases during this second phase,the time period $T$ decreases.Therefore,the time period $T$ first increases and then decreases.

$A$ hollow pendulum bob filled with water has a small hole at the bottom through which water escapes at a constant rate. Which of the following statements describes the variation of the time period $T$ of the pendulum as the water flows out?

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