A hollow sphere is filled with water through the small hole... | Physics | SolveeIt | Solveeit

Today, August 24

Question

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

A

continuously decrease

B

continuously increase

C

first decrease then increase

D

first increase then decrease

Answer

first decrease then increase

Explanation

Solution

The time period of the pendulum
$T=2 \pi \sqrt{l / g}$
$\Rightarrow T \propto \sqrt{l}$
Initially the centre of mass of the sphere is at the centre of the sphere. As the water slowly flows out of the hole at the bottom, the CM of the liquid (hollow sphere) first goes on downward and then upward. Hence, the effective length of the pendulum first increases and then decreases.