Find distance of centre of mass of solid hemisphere of radius 8cm from centre

Options

A. 3 cm
B. 3/8 cm
C. 4 cm
D. 2 cm

Answer

To find the distance of the center of mass of a solid hemisphere from its center, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Geometry**:
- We have a solid hemisphere with a radius \( r \). The center of the flat circular base of the hemisphere is at point \( O \), and the center of mass \( C \) is located along the vertical axis from \( O \) to the flat face.

2. **Identify the Formula for Center of Mass**:
- For a solid hemisphere, the distance of the center of mass from the flat face (the base) is given by the formula:
\[ h = \frac{3r}{8} \]
- Here, \( h \) is the distance from the flat surface to the center of mass, and \( r \) is the radius of the hemisphere.

3. **Substitute the Given Radius**:
- The radius of the hemisphere is given as \( r = 8 \, \text{cm} \).
- Substituting this value into the formula:
\[ h = \frac{3 \times 8}{8} \]

4. **Simplify the Expression**:
- Simplifying the expression:
\[ h = \frac{24}{8} = 3 \, \text{cm} \]

5. **Conclusion**:
- Therefore, the distance of the center of mass \( C \) from the center \( O \) of the hemisphere is \( 3 \, \text{cm} \).

### Final Answer:
The distance of the center of mass of the solid hemisphere from the center is **3 cm**.

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