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 flows out of the hole at the bottom, the period of oscillation will:
(A) Continuously decrease
(B) Continuously increase
(C) First decrease and then increase
(D) First increase and then decrease

Answer 1

Hint:First we have to use the formula of time period due to oscillation where it gives the relation between lengths of the hollow sphere and the acceleration due to gravity. Where the length is directly proportional to the length of the hollow where and from that we can find the solution to this problem.

Complete step by step answer:
As per the problem we have a hollow sphere filled with water through the small hole in it. It is then hung by a long thread and made to oscillate.
When the water slowly flows out of the hole at the bottom now we need to calculate the time period of the oscillation.
The time period of oscillation we will get,
$T = 2\pi \sqrt {\dfrac{l}{g}} $
$ \Rightarrow T\alpha \sqrt l $
As per the given statement the when the water is filled through the small hole at that time the center of mass of the sphere is at the center of the sphere. Now when the water flows out of the hole at the bottom, the vector of mass of the liquid hollow sphere forest goes on downward and then upward. And as the length of the sphere is directly proportional the effective length of the pendulum first increases and then decreases due to which the time period also increases then decreases.
Therefore the correct option is (D).

Note:Here we have use the formula of the time period which we can define it as the time taken by the pendulum to finish one full oscillation and it is denoted by the symbol T. And another important term in oscillation is distance travelled by the pendulum from the equilibrium position to one side.