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To calculate the moment of inertia \( I \) of a solid sphere about an axis through its center, we can use the following formula:

\[
I = \frac{2}{5} M R^2
\]

where:
- \( M \) is the mass of the sphere, and
- \( R \) is the radius of the sphere.

### Given Data
- Mass, \( M = 50 \, \text{kg} \)
- Radius, \( R = 25 \, \text{cm} = 0.25 \, \text{m} \) (since we convert cm to meters for consistency in SI units)

### Calculation
Substitute the values into the formula:

\[
I = \frac{2}{5} \times 50 \times (0.25)^2
\]
\[
I = \frac{2}{5} \times 50 \times 0.0625
\]
\[
I = \frac{2}{5} \times 3.125
\]
\[
I = 1.25 \, \text{kg} \cdot \text{m}^2
\]

### Answer
The moment of inertia of the sphere is:
\[
I = 1.25 \, \text{kg} \cdot \text{m}^2
\]

Would you like further details, or do you have any questions?

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Here are some related questions to explore this topic further:

1. How does the moment of inertia change if the radius of the sphere doubles?
2. What is the moment of inertia of a hollow sphere with the same mass and radius?
3. How would the moment of inertia change if the mass of the sphere is increased to 100 kg?
4. What are the units of moment of inertia, and why?
5. How is the moment of inertia used in rotational dynamics?

**Tip:** Remember to convert all measurements to SI units (e.g., meters for length) before applying formulas in physics.

What is the moment of inertia of a 50 kg sphere whose radius is 25 cm?

Learn how to calculate the moment of inertia for a solid sphere with a mass of 50 kg and a radius of 25 cm. This problem involves key physics concepts in rotational dynamics and applies the formula I = (2/5)MR^2. Suitable for students in Grades 10-12.

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