Question

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?

• A. $T$ decreases first and then increases
• B. $T$ increases first and then decreases
• C. $T$ increases throughout
• D. $T$ does not change

Answer 1

The correct option is B $T$ increases first and then decreases

The time period is given by:
$T=2\pi \sqrt{\frac{L}{g}}$

$L$ here is the length from the point of suspension to the centre of mass of the bob. Assume the bob is spherical, as the water leaks out, the centre of mass will shift downwards, increasing $L$ and hence increasing the time period.

centre of mass will be back at the geometrical centre (which was its original position when it was full of water), As soon as all the water has leaked out, however, the $L$ will decrease and so will the time period. Therefore, option B is correct.