A particle of mass m is released in a smooth hemispherical bowl from shown position A. Find work done by gravity as it reaches the lowest point B.

Explanation

To find the work done by gravity as a particle of mass \( m \) moves from position A to the lowest point B in a smooth hemispherical bowl, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Initial and Final Positions**:
- The particle is released from point A, which is at the edge of the hemisphere, and it moves to point B, which is at the lowest point of the hemisphere.

2. **Determine the Height Difference**:
- The height of point A from the bottom of the hemisphere (point B) is equal to the radius \( r \) of the hemisphere. Thus, the change in height \( h \) is:
\[ h = r \]

3. **Calculate the Work Done by Gravity**:
- The work done by gravity can be calculated using the formula:
\[ W = mgh \]
- Substituting the height \( h \) we found:
\[ W = mg \cdot r \]

4. **Conclusion**:
- Therefore, the work done by gravity as the particle moves from point A to point B is:
\[ W = mgr \]