B

Step 1: Determine the height from which the water falls. The height at which the water is initially located is \( \frac{a}{2} \).
Step 2: The work done by gravity is calculated using the formula: \( W = mgh \), where \( m \) is the mass of water, \( g \) is the acceleration due to gravity (\( 9.81 \, \text{m/s}^2 \)), and \( h \) is the falling height (\( \frac{a}{2} \)).
Step 3: Substitute the values into the equation:
\( W = m \cdot g \cdot \frac{a}{2} \).
Step 4: The work done by gravity is thus: \( W = \frac{1}{2} \, m \, g \, a \).
Therefore, B.