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The problem from the image asks to "Calculate the buoyant force on a sphere of radius 10 cm submerged in fresh water (water density = 1000 kg/m³)". The gravitational acceleration \( g = 9.8 \, \text{m/s}^2 \).

### To calculate the buoyant force \( F_b \), we use **Archimedes' Principle**:

\[
F_b = \rho \cdot V \cdot g
\]

Where:
- \( \rho \) is the density of the fluid (water in this case),
- \( V \) is the volume of the displaced fluid, which is equal to the volume of the sphere,
- \( g \) is the acceleration due to gravity.

#### Step 1: Calculate the volume \( V \) of the sphere.
The volume of a sphere is given by the formula:

\[
V = \frac{4}{3} \pi r^3
\]

Given the radius \( r = 10 \, \text{cm} = 0.1 \, \text{m} \), we substitute into the formula:

\[
V = \frac{4}{3} \pi (0.1)^3
\]

#### Step 2: Substitute the values.
We can now calculate the buoyant force using the following values:
- \( \rho = 1000 \, \text{kg/m}^3 \) (density of water),
- \( g = 9.8 \, \text{m/s}^2 \),
- \( V \) from the previous calculation.

Let me calculate it now.The buoyant force acting on the sphere submerged in fresh water is approximately **41.05 N** (Newtons).

Would you like further details or have any other questions?

Here are 5 related questions for deeper understanding:
1. How does the buoyant force change if the sphere is submerged in a different fluid, such as oil?
2. What happens to the buoyant force if the radius of the sphere is doubled?
3. Can the buoyant force ever be greater than the weight of the object submerged?
4. How would the buoyant force be affected if the sphere was only partially submerged?
5. How is Archimedes' principle applied in designing ships and submarines?

**Tip:** The buoyant force depends only on the volume of the displaced fluid, not on the material of the submerged object.

Calculate the buoyant force on a sphere of radius 10 cm submerged in fresh water (water density = 1000 kg/m³). The gravitational acceleration is g = 9.8 m/s².

Learn how to calculate the buoyant force on a sphere of radius 10 cm submerged in fresh water using Archimedes' principle. This physics problem involves concepts of fluid mechanics, including calculating the volume of the sphere and using the formula F_b = ρ * V * g. Suitable for students in Grades 10-12.

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