How to model this scenario/circuit with 50Hz interference?
I've come across situations like this when high frequency interference (well out of band) is down converted to in-band by the ADC sample rate. So if you are sampling at 500 Hz, 450 Hz or 550 Hz are both down sampled to 50 Hz.

However, the band pass filter of 50 ohms and 1 uF produces a cut-off frequency of 3.1 kHz so to eradicate (largely) an interfering signal that is a multiple of 500 Hz +/- 50 Hz, that interference has probably got a frequency of substantially in excess of 3.1 kHz.

If the aliasing interference was 100.05 kHz it would produce 50 Hz content at base band after sampling but would be substantially reduced when applying the 1 uF capacitor. An example of sampling (blue) an out-of-band signal (red): -



In effect the 1 uF capacitor and 50 ohm resistor are a weak type of anti-aliasing filter.