A

Step 1: Identify the parameters.
- Mass of the piston (m) = 50 kg
- Compression of the spring (x) = 50 mm = 0.05 m
- Area of the piston (A) = $\pi r^2$ (where r = 5 cm = 0.05 m) = $\pi (0.05)^2 = 7.85 \times 10^{-3} m^2$

Step 2: Calculate the force exerted by the weight of the piston.
Force (F) = m * g = 50 kg * 9.81 m/s² = 490.5 N

Step 3: Calculate the work done by the air on the piston using the formula for work done on a spring:
Work done (W) = \( \frac{1}{2} k x^2 \)
Here, we first need to find k. Since F = kx, we find k = \( \frac{F}{x} = \frac{490.5}{0.05} = 9810 N/m \)

Step 4: Substitute k back into the work formula:
W = \( \frac{1}{2} \cdot 9810 \cdot (0.05)^2 = \frac{1}{2} \cdot 9810 \cdot 0.0025 = 12.2625 J \)

Therefore, the work done by the air on the frictionless piston is approximately 12.26 Joules.