To find the natural frequency of small oscillations of the hollow spherical ball, we can use the concept of buoyancy and the equation for the natural frequency of a simple harmonic oscillator.

1. Buoyancy and Submerged Volume:
- The buoyant force acting on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.
- In this case, the buoyant force acting on the ball is equal to the weight of the water displaced by the submerged volume of the ball.
- Since half of the volume of the ball is submerged, the submerged volume can be calculated as follows:
- Submerged Volume = (1/2) * Volume of the ball

2. Equation for Natural Frequency:
- The equation for the natural frequency of a simple harmonic oscillator is given by:
- ω = √(k/m)
- where ω is the natural frequency, k is the spring constant, and m is the mass of the object.

3. Equivalent Spring Constant:
- For a floating object, the buoyant force acting on the object acts as a restoring force, similar to a spring.
- The equivalent spring constant can be calculated using Hooke's Law:
- F = k * x
- where F is the restoring force, k is the spring constant, and x is the displacement from the equilibrium position.
- In this case, the restoring force is equal to the weight of the submerged volume of the ball, and the displacement is equal to the depth to which the ball is submerged.
- The equivalent spring constant can be expressed as:
- k = (Weight of submerged volume) / (Depth of submersion)

4. Weight of Submerged Volume:
- The weight of the submerged volume of the ball can be calculated as follows:
- Weight of submerged volume = (Density of water) * (Volume of submerged volume) * (Acceleration due to gravity)
- Since the density of water is given as 1000 kg/m^3 and the acceleration due to gravity is 10 m/s^2, the weight of the submerged volume becomes:
- Weight of submerged volume = 1000 * (Volume of submerged volume)

5. Volume of Submerged Volume:
- The volume of the submerged volume can be calculated as follows:
- Volume of submerged volume = (4/3) * π * (Radius of ball)^3

6. Depth of Submersion:
- Since half of the volume of the ball is submerged, the depth of submersion can be calculated as follows:
- Depth of submersion = (1/2) * (Diameter of ball)
- Diameter of ball = 2 * (Radius of ball)

7. Calculation:
- Substituting the values into the equations, we have:
- Volume of submerged volume = (4/3) * π * (20 cm)^3
- Depth of submersion = (1/2) * (2 * 20 cm)
- Weight of submerged volume = 1000 * [(4/3) * π * (20 cm)^3]
- Equivalent spring constant, k = (Weight of submerged volume) / (Depth of submersion)
- ω = √(k/m)

- Calculating the values and rounding off to 2 decimal places, we find that the natural frequency of small oscillations of the ball is