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 (COM) of a solid hemisphere from its center, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Geometry**:
- A solid hemisphere is half of a sphere. The center of mass of a solid hemisphere lies along the vertical axis of symmetry.

2. **Use the Formula for the Center of Mass**:
- The distance of the center of mass (d) from the flat circular face of the hemisphere is given by the formula:
\[ d = \frac{3R}{8} \]
where \( R \) is the radius of the hemisphere.

3. **Substitute the Given Radius**:
- In this problem, the radius \( R \) is given as 8 cm.
- Substitute \( R \) into the formula:
\[ d = \frac{3 \times 8 \text{ cm}}{8} \]

4. **Calculate the Distance**:
- Simplifying the equation:
\[ d = \frac{24 \text{ cm}}{8} = 3 \text{ cm} \]

5. **Conclusion**:
- Therefore, the distance of the center of mass of the solid hemisphere from its center is 3 cm.

### Final Answer:
The distance of the center of mass of the solid hemisphere of radius 8 cm from the center is **3 cm**.