The correct answer is option 'D' - first decreases and then increases.

Explanation:

1. The Period of a Simple Pendulum:
The period of a simple pendulum is the time taken for one complete oscillation. It depends on the length of the pendulum and the acceleration due to gravity. The formula for the period of a simple pendulum is given by:

T = 2π√(L/g)

Where:
T = Period of the pendulum
π = Pi, approximately 3.14159
L = Length of the pendulum
g = Acceleration due to gravity

2. Effect of Water Flow on the Frequency of Oscillation:
When the hollow sphere is filled with water and hung as a simple pendulum, the effective length of the pendulum changes as the water flows out of the hole at the bottom of the sphere. This change in length affects the frequency of oscillation.

3. Initially:
Initially, when the hollow sphere is filled with water, the effective length of the pendulum is the length of the thread plus the radius of the sphere. Let's assume this length to be 'L1'.

4. Water Flowing Out:
As the water flows out of the hole at the bottom of the sphere, the effective length of the pendulum decreases because the water level inside the sphere decreases. Let's assume the new effective length to be 'L2'.

5. Decrease in Effective Length:
Since the effective length of the pendulum decreases, the period of oscillation also decreases, according to the formula mentioned earlier. As the water level decreases further, the effective length continues to decrease, resulting in a decrease in the period of oscillation.

6. Minimum Period:
At a certain point, the water level reaches a minimum, and the effective length of the pendulum is at its minimum value. Let's assume this length to be 'Lmin'.

7. Increase in Effective Length:
After reaching the minimum value, as more water flows out of the sphere, the water level starts rising, increasing the effective length of the pendulum. This increase in the effective length leads to an increase in the period of oscillation.

8. Maximum Period:
At a certain point, when all the water has flowed out of the sphere, the effective length of the pendulum becomes the length of the thread alone, which is greater than the length when the sphere was filled with water. Let's assume this length to be 'Lmax'.

9. Variation in Frequency:
Therefore, as the water flows out of the hole at the bottom of the sphere, the frequency of oscillation initially decreases and then increases. This variation in frequency is due to the change in the effective length of the pendulum as the water level inside the sphere changes.

In conclusion, the correct option is 'D' - first decreases and then increases.

Introduction:
In this scenario, we have a hollow sphere filled with water, which is then hung by a long thread to form a simple pendulum. As the water flows out of a hole at the bottom of the sphere, we need to determine how the frequency of oscillation of the pendulum will be affected.

Explanation:
To understand how the frequency of oscillation changes, let's consider the key factors involved:

1. Length of the pendulum: The length of the pendulum is determined by the distance between the point of suspension and the center of mass of the sphere. As the water flows out, the center of mass of the sphere shifts downwards, effectively reducing the length of the pendulum.

2. Effective gravitational force: The effective gravitational force acting on the pendulum is the weight of the sphere plus the weight of the water inside it. As the water flows out, the weight of the sphere remains constant, but the weight of the water decreases. Therefore, the effective gravitational force acting on the pendulum decreases.

Effect on frequency:
The frequency of oscillation of a simple pendulum depends on the length of the pendulum and the effective gravitational force acting on it. Based on the changes mentioned above, we can deduce the following:

1. Length of the pendulum: As the water flows out, the length of the pendulum decreases. According to the equation for the period of a simple pendulum (T = 2π√(L/g)), a decrease in length leads to a decrease in the period of oscillation.

2. Effective gravitational force: As the water flows out, the effective gravitational force acting on the pendulum decreases. According to the same equation mentioned above, a decrease in the effective gravitational force also leads to a decrease in the period of oscillation.

Conclusion:
Both the length of the pendulum and the effective gravitational force decrease as the water flows out of the hollow sphere. Since both of these factors contribute to a decrease in the period of oscillation, the frequency of oscillation will first decrease and then increase as the water flows out. Therefore, option 'D' is the correct answer.