C

Step 1: To find the potential difference (V) induced across the two ends of the rod, we use the formula derived from Faraday's Law of electromagnetic induction. The potential difference can be calculated using the equation:
V = B l v
where:
- B is the magnetic field strength,
- l is the length of the rod,
- v is the velocity of the rod.

Step 2: Consider that as the rod falls with velocity 'v', it cuts through magnetic field lines resulting in the induced emf. The direction of the induced emf can also be determined by the right-hand rule: the thumb points in the direction of motion (downward), and the fingers point in the direction of the magnetic field (usually taken as horizontal), thus giving the direction of the induced emf.
Step 3: The final potential difference induced across the rod will thus be V = B l v.

Hence, looking at the provided options, it closely resembles Option C which represents the correct induced potential difference. Therefore, the answer is C.